book-recommendations

[vital bane]

Welllll Lee's Intro to Riemannian Manifolds is differential geometry Lee's Smooth manifolds is differential topology technically

[tender cobalt]

Lee (Topological manifolds) vs Munkres

[vital bane]

Why not both?

simply do all topology books at the same time

[tender cobalt]

Btw just saw topological proof of infinitely many primes

[vital bane]

Oooh I've heard of it

what's the topology's name

austernberg topology or something

on the integers

[tender cobalt]

Furstenberg

[vital bane]

Oh right Furstenberg

bro came up with it when he was in undergrad 🗣️

[tender cobalt]

dang what am i doing with my life

[vital bane]

I mean

if you're not winning a fields medal in two different fields by the age of 15...

have you ever really succeeded?

[tender cobalt]

too late...

wait can i prove topologically the irrationality of sqrt(2)

🤔

[vital bane]

Time to give up on mathematics and become a filthy engineer and cry with my stacks and stacks of cash about how I couldn't become a mathematician

[vital bane]

I saw a "number theoretic" proof of it in dummit and foote section 0.2

[molten gulch]

I assume it was the contradiction where we let it be some hypothetical a/b?

[vivid elm]

Wait till you realize engineering maths are just as hard as pure maths

[tender cobalt]

bro EEE people solve crazy differential equations

[still panther]

it is unclear how you would define it topologically

it does not have any special topological properties

so probably no

[tender cobalt]

How hard is Lee's topological manifolds exercises?

[trail hemlock]

they are pretty straightforward imo

well

Lee has exercises and problems

exercises come right after a theorem and are usually pretty easy

the problems are at the end of the chapter and are usually a little more challenging

e.g.

[gray gazelle]

Munkres is great, never read Lee

[gray gazelle]

Fun fact, it’s homeomorphic to Q!

[gray jungle]

im on team neither, pickup the utoronto notes on topology.

https://www.math.toronto.edu/ivan/mat327/?resources

[vital bane]

Q factorial? how is that defined?

[gray gazelle]

Topology & Groupoids is clearly the best…

[gray jungle]

<@&268886789983436800>

[tender cobalt]

gamma function retriction to Q?

[river tangle]

Guys any book for functional analysis?

[naive lava]

what's ur purpose of learning?

there are million fa books and everyone of them are for diff ppl

[river tangle]

Basically for quantum mech, i saw some need for it while studying QM, i think an introductory to intermediate course would be enough

[remote sparrow]

@verbal ibex books for universal algebra?

[verbal ibex]

Omg ivr been mentioned

Hmm

I personally learned UA using Burris and Sankappanavar, and imo it uses the cleanest notation from what I could tell

Also, the explanations were all very clear and the book is structured really well

However, more in-depth and also using more category-theoretical concepts is the book by Grätzer, although I dislike his notation a lot lol

Those are the main books to start out with

After that I heavily recommend Commutator Theory by Freese and McKenzie

[grim ore]

I hope you don’t mind me asking what is Universal Algebra 😂, i’ve never heard that field

[verbal ibex]

Notably, this uses basically only lattice theory

[verbal ibex]

Its algebra in its most general sense

[grim ore]

Ooo I like the sound of that

[verbal ibex]

Where in group theory you study groups, universal algebra is about whole classes of algebraic structures (mainly those defined by certain formulas), properties of those classes and how these properties relate and interact and stuff

[remote sparrow]

https://link.springer.com/book/10.1007/978-3-319-11478-1

i got this when it was $16

just seemed cool

and i heard it was useful for model theory

[grim ore]

damn inflation goes crazy

[remote sparrow]

no it was one of those random unannounced sales

[grim ore]

Gotcha, that makes a little more sense

[remote sparrow]

sometimes certain UTX paperbacks go on sale for $16

[verbal ibex]

Both way around

I use model theory too, as universal algebraist

[grim ore]

Yeah someone mentioned a springer discount code in here and i took full advantage with 2 new books

[remote sparrow]

no code needed

just happens every now and then

also some gtm paperbacks as well

[verbal ibex]

I recently bought category theory in context

Excited to start working through it

[verbal ibex]

Yeah, in universal algebra free algebras (the ones given by the free functor left adjoint) are the connection between algebra and logic so theyre really important

[remote sparrow]

i assume you also know some books on lattice and order theory?

[verbal ibex]

Nope, sadly

[verbal ibex]

Im sure theyre not too hard to find though

[molten gulch]

@remote sparrow we had some books lying around for lattices, I'll try to look for em tonight

[remote sparrow]

#book-recommendations message

in fact i already found some through google, but i wanted to know if there were any other references beyond what i found

[molten gulch]

Ahh oki

[rough umbra]

Which do you guys recommend for classical alg geo between fulton and shafarevich? Or another?

[vital bane]

https://tenor.com/view/hell-emiya-thats-hell-youre-walking-into-gif-27052445

[vast jackal]

umm can you send me the link again plz

[remote sparrow]

https://discord.gg/statistics

[remote sparrow]

https://link.springer.com/book/10.1007/978-1-4757-4383-8

maybe this? it seems to segway better into operator algebra territory more than books that are more aimed for pde people such as brezis

https://www.amazon.com/Analytical-Mechanics-Introduction-Oxford-Graduate/dp/0199673853

@naive lava have you heard of this book

[vast jackal]

you guys do Physics?

or is it like a hobby some sort

[gray gazelle]

wht about calculus by richard courant

[naive lava]

kreyszig's book should be okay for you than

or maybe reed and simon if u want qft stuff

but for a general qm course you won't need to know FA, it doesn't even really come up

[gray gazelle]

yall i have an amazing sieries its not math related but it is amazing its called"the unwanteds" by lisa mcmann 10/10 series

[naive lava]

no, lemme check

uh

why would you want this over goldstein?

longer, except stat mech goldstein covers everything here

and is more standardizied

it's not a perfect book but a good book

[remote sparrow]

i was curious as to its quality

i heard it was more on the mathematical side?

[naive lava]

then why not arnold?

[remote sparrow]

seems it uses basic diff geo of curves and surfaces right off the bat

[remote sparrow]

was just curious

[naive lava]

ah i see

[vital bane]

ye you'd need to be good with abstract linear algebra more than anything

[vital bane]

Sour Drop is basically like Thanos collecting infinity stones

he wants infinity books

[verbal ibex]

Gimmee

[vast jackal]

I wonder if sour drop doesn't get tired recommending books

[naive lava]

abstract linear algebra? u mean "let's call this ket and bra without giving definitions"

adjoint? what's that?

dual space, reflexive? naah they are the same lol idk what ur on about

[trail hemlock]

yeah i remember reading ts it’s good

[gray gazelle]

Marry me

[trail hemlock]

•LMAO

ts was like 7 years ago or maybe longer

like i was in elementary

[heady ember]

No. To compare Sour Drop to Thanos would be akin to comparing the Sun to a photon.

One has practically infinite greed, while the other only has 5-greed.

[remote vortex]

And infinity time to read them

[molten gulch]

I could not find them sadly 😭

[verbal ibex]

Crying

[dim pendant]

In other words, you are more interested in logic than in naive analysis. Reasonable.

[uncut surge]

Hi guys I really love maths but I am bad it at the same time how to improve myself need guidance ( I aspire to be an engineer will join college in next few months)

[harsh matrix]

Hi

more like a basic request ig but i need books that can help with math olympiads and stuff

like word problems stuff

[graceful dawn]

Good PDE book for self study?

[grim wolf]

Does anyone have good graph theory books for self study? (Aimed towards math competitions)

[remote sparrow]

https://old.maa.org/press/maa-reviews/measure-theory

@vital bane

[stuck breach]

Does anyone have a book recommendation for number theory?

[grim wolf]

Modern Olympiad Number Theory by Aditya Khurmi

[stuck breach]

Cool, thanks

[dim pendant]

Number theory for beginners by Andre Weil

[stuck breach]

There seems to be a free PDF available

on this page https://artofproblemsolving.com/wiki/index.php/Mathematics_books

[sharp latch]

depends on your level. If you have real analysis experience I’d check out Evans

[marsh blaze]

Hey, I am looking for good introductory texts in geometric analysis. Any recs?

[gray jungle]

whats your background?

[vast jackal]

,books

[remote sparrow]

no

[vital bane]

bro is throwing in Royden slander in the middle of reviewing Cohn

[hollow bridge]

I think the one by W. Strauss is nice if you enjoy applications and haven't studied the subject before

[shadow bay]

does someone have interemdiate coutninga nd probability by aops online pdf? 😭

[fresh skiff]

Sour Drop

any recommdation for number theory (elementary)

[blazing rune]

Hans Rademacher's Lectures on Elementary Number Theory is pretty old, but it's short and covers the basics.

[fresh skiff]

I will check

Thank you

[kindred sequoia]

Calc 1 textbook

[molten gulch]

Thomas' Calculus

[tender cobalt]

Thomas' best

[gray gazelle]

Whats a good abstract algebra book that develops the theory straight from the ZFC-Axioms (no prerequisites) and has good exercises?
For reference I really like how the exercises from Analysis by Terrence Tao are and Ive enjoyed reading a bit of Set Theory by Jech. I also like abstraction and rigour.

[lapis heart]

Why from ZFC. ZFC puts set theory on solid foundations. Abstract algebra only needs to assume those foundations

So abstract algebra from elementary set theory foundations (basically the approach u see anywhere) is good enough

[gray gazelle]

I dont know if my understanding of the foundations is good enough. Im currently learning Analysis by Tao and read the beginning of Set Theory by Jech (up till the aleph numbers)

[lapis heart]

Then read a set theory book for that

idk

[gray gazelle]

What would you recommend as a prerequisite for abstract algebra then?

[lapis heart]

just some intro to proofs book does it

[vast jackal]

any recs for modern algebra

[vast jackal]

Also what's the prerequisite for modern algebra

[gray gazelle]

Will the used number systems be constructed in abstract algebra books?

[lapis heart]

[gray gazelle]

(assuming the naturals/ordinals)

[lapis heart]

u dont use no number systems except 1, 2, 3

what

the first things u learn about are groups rings fields in no particular order

ordinals arent rlly relevant

[gray gazelle]

oh so things like the definition of the rationals and the construction of the reals via dedekind cuts arent that important?

if so ignore the things ive typed
the book only needs to have good exercises and be rigorous

[lapis heart]

no

even for analysis i wouldnt say dedekind cut construction is important

[loud cradle]

the reals are largely irrelevant for abstract algebra
the rationals are relevant for generalizations like the field of fractions

[lapis heart]

u dont actually use it to do stuff with the reals

u just assume the usual properties

ofc learning the construction is educational, etc etc

Math generally, you can black box the building blocks no problem. And go back to figuring out how the blocks work later

[gray gazelle]

Then I think that I know the prerequisites already or can figure them out while reading. What book would you recommend?

[lapis heart]

Thats the thing too. When u come into a roadblock because u blackboxed something u can go back then and there.
Axiom of Choice is necessary for some parts of algebra. You can blackbox it if u want for the proofs, or go back and look a bit deeper

[gray gazelle]

as someone who is learning math for fun that coming back is what ive been doing constantly
good to know it will keep working

[gray gazelle]

Im searching for something with few but really good exercises (Abstract Algebra). I will be self studying

[lapis heart]

#books

this archive could be relevant

i dont have any recommendations

[gray gazelle]

I dont have access

[lapis heart]

archiver role

[gray gazelle]

Ill look into it
thank you

[full cairn]

Imo almost all intro algebra texts have good exercises. If you want something with (partial) solutions you could go for either Gallian, Aluffi's Notes from the Underground or Bhattacharya. Fraleigh is also good for self studying

[remote sparrow]

#book-recommendations message

[tender cobalt]

You can start without any prerequisite, most beginner books dont assume anything

Nice beginner books are Aluffi's "Algebra Notes From Underground", Fraleigh "A first course in abstract algebra" , Artin "Algebra" (its a bit harder but also you can read it without any prereq)

[gray gazelle]

Which one of them goes into more detail?

[tender cobalt]

Aluffi is very beginner friendly

also has some solutions in the back, aimed at self learners

[gray gazelle]

Is it still rigorous?

[tender cobalt]

100%

[gray gazelle]

Looks like the perfect book to me
Thank yall for the recommendations

[tender cobalt]

very beginner friendly and shows all steps for theorem proofs instead of saying "its obvious to see" etc

which one is most advanced here?

[gray gazelle]

damn it cant get any better

[remote sparrow]

i think a few older texts do this, but i don't remember. if you're curious to the full constructions of various number systems, you can look here: https://www.amazon.com/Number-Systems-Foundations-Analysis-Mathematics/dp/0486457923

[remote sparrow]

nzm

[full cairn]

Yeah, Aluffi is a good choice. It has a more categorical viewpoint than the others, and starts with rings instead of groups

[tender cobalt]

starts with rings and integers as well

[tender cobalt]

Yeah

Goes into module after rings, which most first courses do not

Also again, no linear algebra assumed too

[molten gulch]

Isn't this only in his grad book

Or am I stupid

[tender cobalt]

No

[remote sparrow]

https://www.amazon.com/Algebra-Notes-Underground-Paolo-Aluffi/dp/1108958230

[tender cobalt]

his grad book starts with groups

[molten gulch]

Ah okay

[gray gazelle]

Wait so which book do I need to read?

[tender cobalt]

The one Sour Drop has linked ^

[gray gazelle]

okay

[tender cobalt]

his grad book is called "Algebra: Chapter 0" its more advanced, not for beginners

[remote sparrow]

https://www.math.fsu.edu/~aluffi/undergrounderrata.2021/Errata.html

please keep the errata sheet in mind

[full cairn]

btw, when you're self studying it may be hard to know what material to skip and what is important. You probably don't need to read Aluffi cover to cover, you can consider skipping some of the more advanced ring theory stuff in the middle, and skip straight to groups or modules when you're ready

[tender cobalt]

when youre self studying, its actually better to finish a book

than worrying about skipping

[full cairn]

the group theory is pretty fun, so when you're sick of ring theory it's nice to mix it up

[tender cobalt]

that way, you get proper foundations laid down before going to more advanced topics

[tender cobalt]

yeah fair

[full cairn]

yeah, in an ideal world you should finish every book, but in practice you're gonna spend so much time on stuff that is not super important

[gray gazelle]

so group and ring theory dont depend on each other? (in the context of the book)

[remote sparrow]

they do depend on each other

[full cairn]

like Noetherian and Artinian rings, finitely generated vs finitely presented, etc. are not that important to understand on a first read-through

[remote sparrow]

however, whether to introduce one or the other first is a pedagogical choice

[full cairn]

you can always learn about it later

[gray gazelle]

I see

[tender cobalt]

i dont think these stuff are in aluffi notes from underground

oh wait it is

[remote sparrow]

generally, authors like to treat rings as specific examples of groups

[tender cobalt]

@gray gazelle what is your background? like what math do you know rn

[remote sparrow]

since rings satisfy all the group axioms as well as some others

[full cairn]

yeah, Aluffi even introduces exact sequences at some point I mean, it's nice to get some exposure to it, but I don't think you need to understand it fully on your first read

[gray gazelle]

Chapter 8 in Analysis 1 by Terrence Tao and the first pages of Set Theory by Jech (till the aleph numbers)
I really liked the rigour in the book by Jech I didint read it further cuz Im not that interested in set theory

[tender cobalt]

Average pure math experience, just copy paste definition

[tender cobalt]

You can also try giving Artin a shot, although theres no solutions in the back

[old elk]

HAHAHAHA

[full cairn]

Am I missing something, what's so funny? 🤔

[naive lava]

so, i haven't finished alluffi yet

but i am interested in algebraic geometry

i don't wanna hang myself so i won't be reading hartshorne

any other recs with similar coverage to hartshorne

(i don't know french also don't wanna read 1800 pages)

[strange tree]

https://agag-gathmann.math.rptu.de/en/alggeom.php and The Rising Sea are the usual recomendations for this

[naive lava]

yeah i was thinking of vakil

is is good?

and what exactly are the prerequisites?

[remote sparrow]

gortz and wedhorn

@dapper root

[old elk]

It makes me laugh because when I downloaded the book I thought it was easy but it is not.

[old elk]

a lot of algebra

[naive lava]

so im assuming aluffi wouldn't be enough?

[remote sparrow]

i heard vakil was supposed to be self contained wrt the commutative algebra

[naive lava]

hmm

[remote sparrow]

but it couldn't hurt to read eisenbud or matsumura first

[naive lava]

comparison between grotz and vakil?

[old elk]

I'm talking about this lie

[remote sparrow]

or altman and kleiman

[naive lava]

800 pages 💀

[remote sparrow]

u just need a subset

[naive lava]

which subset?

[remote sparrow]

think he says in the preface

[naive lava]

ah

i see

thanks!

[remote sparrow]

if u don't wanna think about it just do altman and kleiman

basically modern atiyah macdonald with all solutions

[naive lava]

whaaat?

seems like a treat

[remote sparrow]

free online

[naive lava]

every textbook is free online

also, do you know how grotz and vakil compares?

[remote sparrow]

there are some i couldn't find

[naive lava]

well you collect unprinted books lol

[remote sparrow]

not rly, it's just mentioned here

pretty sure chmonkey recommended it

[naive lava]

ah i see

i'll try to find the original post, thanks!

[full cairn]

Yeah, the title is a cruel joke I dare not imagine what Chapter 1 is like

[past dust]

Proof based calc book ?

[mossy flume]

Vakil or Gortz & Wedhorn

probably keep both on your shelf and refer to both

[remote sparrow]

spivak, apostol, and kitchen

[fresh skiff]

Thank you

[tender cobalt]

Kitchen?

[remote sparrow]

https://www.amazon.com/Calculus-Variable-Dover-Books-Mathematics/dp/0486838064

[molten gulch]

Leaping off current math-discussion, does anyone know of any books on euclidean geometry, conics, quadrics, etc.. that are NOT Euclid (tho idk how much of what I just said is actually covered in euclid)?

[mortal ore]

euclid's elements is pretty good

[molten gulch]

I struggled a LOT with reading it the last I did due to the way stuff is wording and stuff

[mortal ore]

oh i was just trolling since u asked for not euclid

[molten gulch]

oh buh

[mortal ore]

would you be mad at me if i said i didnt know any other geometry texts

[molten gulch]

but seriously, idk of any books that cover stuff like conics and quadrics heavily outside of like...idk AG books

[molten gulch]

no lol

That's why we have a public book recs channel :) you share what you know

[mortal ore]

eventually ill know AG

seems really high level tho so im not stressing about it

[past dust]

Anyone heard of leithold calculus ?

[remote sparrow]

lang, hartshorne, kiselev, and pamfilos are ones i've heard of

[marble solar]

Was able to write off much of my book purchasing as taxes

So if you didn't include it in your tax forms, just know that you can

[remote sparrow]

how'd you do it

it's my first time

[mortal ore]

i knew if i became a mathematician id be joining the tax fraud community

[marble solar]

Mandatory: am not a CPA, but there was a spot in turbo tax to upload materials spent on courses

It just asked for an amount

[molten gulch]

How gentle do these begin? We were never all too good at this material and don't want to explode on contact

[remote sparrow]

they are all suitable for high schoolers. probably more concise than the ones assigned in today's schools though

try kiselev first

[molten gulch]

Will do, thank you

[brisk ice]

curious are you filing like some business thing or are you writing that like under your personal taxes? Because I would assume maybe standard deductions would be what most people take compared to itemizing

[marble solar]

I'm a PhD student, I'm filing it under the appropriate subject for college students

[remote sparrow]

https://www.rxddit.com/r/math/comments/1jzxzvl/best_graph_theory_book/

[topaz girder]

Hello, I am preparing for a term paper about the Riemann Hypothesis. Would appreciate it if anyone could drop some literature🙂

[mossy flume]

Wait wut

Bruh I should have done this

[remote sparrow]

https://www.youtube.com/watch?v=-vfvIPHMPqU

[old elk]

My advisor has great respect for people who do research in number theory.

[remote sparrow]

what is this video description

[remote vortex]

~~Surely the best calculus book ever written is this: https://www.academia.edu/41616655/An_Introduction_to_the_Single_Variable_New_Calculus~~

[analog aspen]

if anyone starts math from 0, what advice would you give him?

I need a source that is understandable and that I can take plenty of notes from

[unkempt fractal]

Someone perhaps has lecture notes about Coding Theory?

[unkempt fractal]

To have a friend that knows at least as much math as they know so they could use him if necessary

[fresh skiff]

Cool
Damn i wanna do thesis in algebra but we had no professor for pure maths 💔

Now I am working on numerical analysis

[analog aspen]

Yeeah but I want to use my head as much as possible

I like to feel my mind while thinking

[trail hemlock]

cant go anywhere without seeing this 😭 💔

[molten gulch]

What the fucj

[mortal ore]

is this typed in google docs

[trail hemlock]

i think so

prolly word 💔

[remote vortex]

Typical, you criticize the medium because you can't find fault with the message

[trail hemlock]

well its not without merit if read as a study of schizophrenia

[mortal ore]

it was just the first thing i noticed

[unkempt fractal]

Someone perhaps has lecture notes about Coding Theory?

[mystic orbit]

Mofo is nerfed 5 times

[trail hemlock]

what do u even mean by this.

[unkempt fractal]

How did you get 5 times 😟

[mossy flume]

I have this saved from when my math and TCS club from undergrad did a series of presentations on coding theory

• Essential Coding Theory by Venkatesan Guruswami, Atri Rudra and Madhu Sudan
• Courses taught by Venkatesan Guruswami, including some on Coding Theory
• Sphere Packings, Lattices and Groups by J. H. Conway , N. J. A. Sloane
• Cool YT Channel with a playlist on Algebraic Coding Theory
• ECE 556 SP 2020, a course on Coding Theory

far from exhaustive ofc

[naive lava]

hey c'mon

you can make that rigorous in string theory

as rigourous as renormalization can get

[floral lantern]

Renormalization has a mathematically rigorous treatment 😭

Also - anyone have thoughts on Jarvis ANT?

[blazing rune]

I'll add a book relating it to algebraic geometry (hot topic in coding theory, database redundancy, and other topics these days): Van Lint, J., & Van der Geer, G. (2012). Introduction to coding theory and algebraic geometry (Vol. 12). Birkhäuser.

[trail hemlock]

🤓

[floral lantern]

😔

do you know what doesn't

path integrals!

[old elk]

Where do you come from?

At my university there are no professors specialized in pure mathematics.

[fresh skiff]

Ohh. I am from Pakistan
(Particularly in the state where i live, education is really low)

[ancient sand]

mathematical analysis: a concise introduction by bernd schroder is very good

[spare loom]

Hi guys is there a math book that teaches you the basics of engineering pls

[chilly hound]

can someone recommend a book to learn the calculus needed for physics? ill be reading electrodynamics by griffith which has multivariable calc and partial differential equations and stuff

[vast jackal]

Stewart's calculus should suffice

or thomas

there's alot

and they're msotly the same

or if you want something challenging do apostol

or you could try out Thompson's calculus which is pretty unique

[molten gulch]

There's also spivak's calculus which AFAIK is decently challenging

[vast jackal]

yea pretty challenging

spivak's is like a intro to anal

[trail hemlock]

honors calculus by maccluer

slept on fr

[vast jackal]

I've also wondered what's anal the first time in math lol, and then aha it was short for analysis

[tender cobalt]

@fair fiber yo is sweden good

how are the university costs there

well thats 10x cheaper than america or uk xd

8000 / year?

Well that's still cheap compared to USA

are there scholarship/financial aid programs for international students? my main target is germany since its really cheap

I will learn

I see

[vast jackal]

yea it depends on the city you're in

especially like Berlin or smth

[topaz girder]

Same, thought I was the only one, who likes it, when it gets warm and void

[vast jackal]

Just do lots of problems, that's what I hear all the time, Do hard problems, easy ones, and etc doesn't matter

when I do problems I see lots of holes in my knowledge

[topaz girder]

What about munich or Heidelberg?

[tender cobalt]

Ye thats where I wanna go

[fresh skiff]

Yeah probably i am thinking to go outside for master and higher education. (My undergraduate has been fucked up by my university so i don't wanna waste masters and phd)

I am thinking for Germany (Bonn university) and maybe Italy (we get a scholarship for Italy i will apply for it)

Idk if there is any scholarship for Germany (particular Bonn university)

Sorry for this question, are u from Germany?
(If u don't wanna answer you can skip it)

Oh ok.

Well i am already in my final year 😵‍💫

I should keep Searching for scholarships

Idk where should I focus, IELTS or Germany lol

[reef granite]

anyone read "surely you are joking my feynman"?

[fresh skiff]

Oh yeah
||Btw i am scared of large spiders 💔||
I will try to come out from Pakistan, thank you mq

[west spoke]

Austria is not Australia, I doubt there’s large spiders in Austria

[fresh skiff]

Oh my bad.

True, but I dont wanna waste my time.

I have already wasted 3.5 years now i am trying to improve my few main subjects like
(Real & complex analysis, abstract and linear algebra, topology and differential geometry)

(i think we should move to #advanced-lounge or #math-discussion

[naive lava]

not so sure about math education but it has a very nice math phy program

[tender cedar]

guys

what is a good number theory book that encompasses both "elementary concepts" and "advanced concepts"?

I'm looking for a overall good number theory book

[floral lantern]

Advanced concepts as in abstract algebra?

Typically number theory books are in two sets - pre-abstract algebra and post-abstract algebra

[stray veldt]

you can check https://link.springer.com/book/10.1007/978-3-030-98931-6

[tender cedar]

yeah

I would say so

[tender cobalt]

yoo this is cool

[tender cobalt]

any more books like this?

[weary bison]

Hey, silly question. Is Michael Artin's Algebra also a good linear algebra textbook or should I look elsewhere?

I'm looking more to review what I remember learning, if that helps narrow down what I'm looking for

[graceful moon]

If youre just looking to review what you know id recommend Hoffman Kunze, its a little more concise (since its just LA) and just generally a great book

Artin is good too though, just generally

[weary bison]

Thank you!

At first I was trying to learn linear and abstract algebra in one go, but apparently the university I'm applying to has an entrance exam on LA and Real Analysis

[weary bison]

The Real Analysis textbook I was recommended was Tom Apostol, but I'm also open to recommendations there

[weary bison]

Although in that case, I need to learn from scratch so I'd need an introductory textbook

[ocean hemlock]

i like the aops algebra books

but make sure to look at the book in sections

or you'll get bored

[naive lava]

apostol is nice

or so i head

but abbott is great

if ur looking for something concise than rudin might also work

[floral lantern]

Ireland and Rosen?

A little more on the advanced than elementary side

But it does plenty of ENt and the first 6 chapters require almost no algebraic formalism

[slender cargo]

Abbott is a standard recommendation for a friendly intro. I've used it, and I've been thinking it's the best book to use as an intro compared to the others I've sampled

[weary bison]

Thank you!

[merry sphinx]

abbott, jay cummings, lebl are good

[remote sparrow]

why would they do that? your uni pays a handsome sum to subscribe to the digital library and make books available

small-scale downloading, even in the hundreds, won't hurt them

[remote sparrow]

i've been assigned a springer book a couple of times

[terse garnet]

How do yall study? is it recommended to do all the exercises in the math book or be conservative and only do a selected few?

[gray jungle]

Despite popular belief (looks at you @vital bane @heady ember ) no, you should select the exercises you do.

[heady ember]

I do select the exercises I do: all the nontrivial ones

[terse garnet]

I think im just gonna do the example problems that the book gives you while reading the lesson

I think breadth beats depth

[vital bane]

and post algebraic geometry

[vital bane]

bad idea

[vital bane]

certainly not that...doesn't even make sense

[floral lantern]

elliptic curves 💀

[cunning elk]

yall do textbook exercises? 😭

[vital bane]

I mean obviously you don't have to do every single exercise in a math textbook, but doing as many as you can given a (actual or artificial) time constraint is a good idea

[cunning elk]

me outing myself for slacking 💀

[vital bane]

70% of the learning happens while doing problems

[cunning elk]

true true

i just struggle to make the time to do them

bc double major

[vital bane]

gotta work twice as hard

[cunning elk]

math + piano

[vital bane]

piano major?!?!

you mean music major?

[cunning elk]

yuh

at one of the top US music schools

the uni it’s a part of has uh

the math department of all time

[vital bane]

oh the music school has like a uni integrated into it? it's not just for music?

[cunning elk]

it’s part of a large university ye

[vital bane]

inchresting

[cunning elk]

also the textbook exercises they do assign

are always the trivial early ones at the start of each set

😭

and somehow the average on the last midterm was still 55%

(for intro algebra)

(using herstein’s textbook)

despite the fact that my prof was a student of artin 💀

[terse garnet]

I think doing the bare minimum to learn a topic is best since theres so much to learn nowadays

and your expected to learn it quickly

and over time I think doing only problems for topics that are your main point of interest instead of prerequisites seems to build upon the knowledge that you learned from the prerequisites and consolidates your understanding for what you want and what you needed to learn

more in depth

Idk i just think in a black and white way

you either do all the problems or you do the bare minimum

to pass

since its very arbitrary to do the problems in a limited way since you have no way of knowing which problem will make you learn the most since you dont know if your just self studying

maybe if your doing a uni course and you have a professor pick out problems from his expertise that will give you the most bang for your buck it wud be worth

idk i just think since there are no specific set of problems that would give you total understanding you might as well do the minimum set of problems to give you conceptual understanding

which would be the exmpl probs in my case and the books im reading

you might have a book without exmpl probs so idk what u wud do then

just take an hour timeslot of doing problems i guess

[vital bane]

this is a very bad mindset in general. "i dont know if I would get the best possible outcome even if I put in effort, so I might as well not try 🤷‍♂️" you should try to break out of it.

[mortal ore]

You can possibly gain a lot of knowledge from putting in effort, but you know you wont gain much from not trying at all

[terse garnet]

I just think if my goal is a specific topic I don't wanna get bogged down by prerequisites when I could strengthen my understanding of the prereqs doing the target topic

[ripe axle]

I have a great book for y'all

https://en.wikipedia.org/wiki/List_of_common_physics_notations

[vital bane]

this is backwards

you strengthen your understanding of the target topic by strengthening your understanding of all the prerequisites

math is like a ladder, without the bottom rungs you will not be able to reach the higher rungs, and if your bottom rungs are unstable and wobbly, you will have a harder time reaching the top

[heady ember]

Yeah trying to sprint before you can crawl isn't a great idea

Reads langlands papers before learning what is a group
Becomes a crank

[heady ember]

Math is learnt by doing. If you don't practice active reading/doing, then don't expect to learn.

[cunning elk]

i don’t always have the time to but i do try to sit down and work through the examples + exercises

problem is i do it too sporadically 😔

and it comes back to bite me in the ass

[cunning elk]

sure i can do well on exams but my understanding of the material is uh

sus

yeah as described in those quotes

[cunning elk]

now obviously that bodes very poorly for if i decide to do grad school

how do i get myself out of this mess

[remote sparrow]

try asking professors for course materials in advance of the term

and try to at least study a bit of it on break

[cunning elk]

i did a bit of prereading for analysis and it did help

so i should prob do more of that so im not as swamped during the term

[remote sparrow]

try skimming or skipping those intros?

[heady ember]

Just skip it if you know it well

or just skim it

[golden salmon]

If u read a maths book like a narrative u are a mystery to me

I mean sure maths have a sort of abstract story to tell about the objects in them so I kinda get it but also I just start with the exercises and work backwards

[sacred sorrel]

I prefer Birkhoff and MacLane's book

[lost arch]

guys, i know chances are low, but i need notes and problems for this course real bad, lost them somewhere a few years ago and now trying to revise the course's contents. The course is taught in the Math Department for Math majors in Trinity College, Dublin. They used to have an archive that contained this course as well but by now it's gone. If anybody was/is a student there in the Math Department, please, let me know if you have it.

idk why but i cant insert the picture of a course

it's called MAU11202 Advanced calculus

its content is
Vector-valued functions: parametric curves, calculus, change of parameter.
Partial derivatives: definition, chain rule, gradients, maxima and minima.
Multiple integrals: double and triple integrals, surface area.

if anybody knows by any chance a course similar to this, share it with me, please

[signal mountain]

There is no shortage of sources that will cover these topics
Is there any reason it needs to be specifically the notes and problems from the trinity college Dublin course?

[stuck breach]

it was so easy up until section 1.11, example problems, then suddenly it was hard

[tender cobalt]

can I read ireland rosen classic intro to modern number theory after artin

[sacred sorrel]

Yes

ireland has a lot of algebraic concepts

inside the theory and exercise

[tender cobalt]

what will i learn from ireland?

[terse garnet]

so Is the consensus to do as many problems as you possibly can inside the math textbook?

[lost arch]

well i was revising these particular courses, wanted to learn it the way it's supposed to be learnt, cause all the previous courses supply a student with the needed prerequisites

anyway. i would like to cover the mentioned topics with some rigor. could you recommend some books/notes?

[grim ore]

<@&268886789983436800>

[floral lantern]

Yeah but make sure you do the Galois theory

[cunning elk]

yes, learn by doing

[merry sphinx]

has anyone here read "from groups to geometry and back" by Katok and Climenhaga? if so, how was it?

i havent done any AA, i've done analysis and some LA

[remote sparrow]

hubbard or shifrin

[manic sparrow]

haven't finished reading a mind for numbers but it's quite fascinating

[lost arch]

Vector Calculus, Linear Algebra and Differential Forms: A Unified Approach
this one?

[remote sparrow]

https://matrixeditions.com/

buy here

much cheaper than amazon

don't bother with the ebook, they have some shitty drm thing for it

[lost arch]

thx

[graceful moon]

I wouldnt say as many as you possibly can, but a juducious selection certainly

You can't do every problem and likely wouldn't gain much from doing so, but picking a reasonable selection from every chapter is usually a good idea. I tend to pick 2 or 3 problems that look fairly straight forward, an apply the definition type question and a selection of 2-4 problems which look more non-trivial from each chapter. Of course modulate that accordingly, if you have more time, or if you struggled with a section do more, if the section didnt have much of interest do less etc.

[vital bane]

Now it's two

well I suppose you said "my" math program

[vital bane]

I would say as much as you possibly can doing extra problems never hurts

[grim wolf]

Any books on graph theory?

[mossy flume]

Diestel or West's text are the two I've seen recommended the most

[vital bane]

🗿yup I used to absolutely hate math back in 6th and 7th grade

I would cry at the thought of studying math for an exam But eventually I found math content on youtube like Numberphile and 3Blue1Brown and this server 🔥 and saw math for what it actually was

[rain hound]

DRM for content people “buy” is so evil

[rain hound]

Chartrand has good books. There’s a dover one for very cheap.

[gray gazelle]

Same man, everything my perception my likeness changed in 9th for mathematics

[tender cobalt]

whats drm

[signal mountain]

Digital rights management, basically you don't really own the data you have a licence

[rain hound]

DRM should probably more properly be called Digital Restrictions Management

It is institutionalized theft. You will never own what you buy as long as it has DRM limiting your rights. You have a limited license to access the content (for an indefinite period of time) that they can take away or limit further whenever.

[stable flicker]

Laws allow this so /shrug
Thing is Anything as-a-Service allows for annual recurring revenue, which is king in any profitability model

[graceful moon]

I think putting it like that sends the wrong message though. We all have finite time with an infinite number of problems, possibly should include the asterisk of without taking up too much time

[vital bane]

I mean

[graceful moon]

That might seem obvious to you, but I dont think it inherantly is

[vital bane]

within a given time constraint

True you should include that last part

[rocky berry]

please tell me any good book which tells you all about geometry with lot of problems and teaches you to write geometry proofs?

[cunning elk]

no

hundreds of such books have been written

aops intro to geometry might be a good place to start tho

on a more serious note

[rocky berry]

IM ALWAYS SERIOUS 😾

[rocky berry]

thnxx i start from today then, lets hope it will turn out goood

[cunning elk]

it is somewhat more challenging than standard geometry texts but does a better job introducing proofs imo

[rocky berry]

i belive u man! im desperate to study even ifs challenging im ready to take on (frist day motivaion be le*)

but i dont have belief in motivation

[plush knot]

Does anybody have tips on resources regarding mathematics and voting systems? I’ve started digging into balloting systems and winner criterion’s here and there, but it’d be nice to have a comprehensive resource to learn from.

[winter wind]

Doing an reu where ill be studying multisymplectic and polysymplectic forms but i havent ever formally learned about differential forms or manifolds. Any book or resource i can use to get familiar with thr material?

I also may have to work with operads, so any good introductory resource for that would be helpful too

[clever cipher]

idk why i searched for robin hobb in this server but i did and this is one of the most pleasant surprises i could have received

[heady ember]

Obviously, drawing Tikz figures is a more productive endeavor that one strives towards

[remote sparrow]

what book is this

[half void]

anyone have any good books on finite element methods?

[lilac raven]

brenner scott is the canonical text

but it’s kind of difficult

bartels numerical approximation of pdes and braess finite element theory are good too

[half void]

is it up to date

[lilac raven]

it’s 2008 so maybe not the most modern methods

but for general theory of finite element yeah

i think if you mastered that book you could probably understand any modern research paper

[void pasture]

Any combinatorics book for beginners with answer sheets to the questions?

[remote sparrow]

https://www.amazon.com/Walk-Through-Combinatorics-Introduction-Enumeration/dp/9811277842

[void pasture]

How did you feel regarding the book's introduction to concepts?

Does the author start with an example that serves as motivation to the more general concept or?

[remote sparrow]

where appropriate, sure, but a lot of the initial objects and definitions you work with in combinatorics aren't that difficult to grasp

[cunning elk]

i really wish people would stop throwing around the "concept" buzzword

it's been used and abused to the point of being completely meaningless

also i'm not the biggest fan of the bona text for a complete newcomer to combo

[snow locust]

i like pikhal and tikhal

[cunning elk]

i'd almost be tempted to recommend the aops textbooks for a gentler introduction (intro minus the first few chapters which are clearly written for early middle schoolers + intermediate)

[cunning elk]

college level classes don’t mean anything if it’s just calc1

see AoPS’ article on the “calculus trap”, calculus is hardly taught in any substantially rigorous/challenging way in the US

[cunning elk]

if on the other hand they’re taking and performing well in traditional upper level classes like analysis, etc

then that’s smth to take particular note of

[rigid trail]

sad

[tender cobalt]

Honours calculus and multivariable calculus class in UGA (spivak for calculus, shifrin for multivariable)

[signal mountain]

Interested people may read good books or they may just read any old crap they can find haha

It can go both ways 100%

[meager notch]

it can go both ways 100%

source me

[vivid jewel]

whats the best calc tb

[sacred sorrel]

spivak, courant and apostol

[vivid jewel]

no those are big boy textbooks

i want an easy one

[sacred sorrel]

then, you won't learn well

I used Stewart's Calculus

[vivid jewel]

is there a shorter book?

1.3k pages is a lot

[sacred sorrel]

a course of pure mathematics g. h. hardy

[pine tundra]

Maybe it's better if you just select the single topics you wanna learn and google them

Such as "limits and asymptotes lecture notes"

[vivid jewel]

ill just go the textbook route

how is aops calc

ive used aops books before and i like em

[sacred sorrel]

alr

[remote sparrow]

it's three semesters worth of content

[vivid jewel]

damn

it will take atleast half a year to finish that

[merry sphinx]

i mean, thats not bad

for basically 3 courses

[wraith cave]

half a year for 3 semesters is a pretty good deal

[graceful moon]

Yeah, it usually take about that or longer as part of a course. It just kinda is a lot of content.

[floral lantern]

The AoPS book is fabulous

No Calc 3 but imo it’s the best intro to calculus since it combines challenging calculus (not analysis) problems while still having a solid amount of proof based thinking

[rain hound]

stick with rngs and rings

[void pasture]

then go ahead, tell me a better fitting word? Since when did "concept" Become a buzzword? Sure, a concept is a collection of releated thoughts, often thought-out and structured but it is not equivalent to theory. You are right here, but does it really matter?

[remote sparrow]

@old elk

[trail hemlock]

@

[cunning elk]

see: chatgpt’s enshittification of k12 math ed

and people throwing around the term while not having the faintest clue what they’re talking about

[low mulch]

Anyone know any good book for someone who use to love math, to gain love in math again

[rigid trail]

a book in a field of math you like

[low mulch]

I see thanks a lot

[remote sparrow]

is your screenshot from a book?

what's the name of it

[dapper root]

The colors surrounding the citations suggest to me this is a paper

[trail hemlock]

damn i thought sour drop would rainbolt the book by recognizing the pixels

[molten gulch]

LOOOL

[trail hemlock]

wait the original message was deleted

😭 bruh

[remote sparrow]

why'd they delete the post? did they think i was getting on their case for posting something that isn't from a book in #book-recommendations?

well i have the image from neam's algebra thread in #groups-rings-fields

i only wanted to know where the source was from

[trail hemlock]

https://www.cip.ifi.lmu.de/~grinberg/t/23wa/23wa.pdf

[remote sparrow]

https://www.cip.ifi.lmu.de/~grinberg/t/23wa/23wa.pdf

[remote sparrow]

thanks

i entered a string from the text

[trail hemlock]

same lmao

[remote sparrow]

it ended up being a book

[dapper root]

Glorified set of lecture notes

I kinda stand by this being a pdf

I really wanted to say that but obviously all these things are PDFs

I just don’t consider something that isn’t getting printed a book

[trail hemlock]

the reaction of after like 2 questions sent me

[remote sparrow]

vakil's rising sea before it got published by PUP: 😭

[old elk]

I believe the book was mentioned above

[remote sparrow]

thanks genius 🙄

[paper salmon]

It's prolly becaues this thing is copyrighted. The structure matches the texts from the Stanford math department so I think it's a textbook for one of their math courses.

oh wait nvm

looks like the link was already given

It does look very similar to the stanford texts tho. Maybe it's just a pdf thing?

[remote sparrow]

i don't think fonts or formatting considerations are necessarily specific to a school

[remote sparrow]

right but they could have given the title and author

or if they didn't know, they could have said "idk"

[daring lake]

stack exchange

[novel hound]

oreilly maybe? although it's probably more software engineering than computer science...

[mortal granite]

Where is a good place to read about modules? I'm currently taking a class on Rings and Modules and we just started learning about modules but there is no provided textbook or reference material. So any book, website or document recommendations would be greatly appreciated.

[marsh ingot]

I was reading about modules a week ago and I like it

[mortal granite]

Thank u sm

[candid cipher]

i'm looking for a book that covers real analysis in R^n. i'm fine if it assumes real analysis in R as a prerequisite

or just in R^2/R^3 instead of R^n is fine too

[daring lake]

Atiyah also got modules

[gray gazelle]

can anyone recommenD book which has good theory FOR JEE EXAM MATHS

and conceptual qns too for beginner to advanced level

[merry sphinx]

munkres, maybe

theres also spivak but youre gonna want to have the errata open

[proud osprey]

Does munkres have an analysis book?

[molten gulch]

no he means just jump to topology

or wait

he does have that manifolds book

[proud osprey]

oh true, the first four chapters are multivariate analysis

I liked Tao as a supplementary book

[merry sphinx]

analysis on manifolds

[gray gazelle]

??

[tender river]

https://classicalrealanalysis.info/documents/TBB-AllChapters-Landscape.pdf this is a fine book, lots of good end of section exercises and every chapter ends with challenges problems some of which have a hint at the end, if its too bulky for you you can still keep it as a side reference

it does do R^2 specifically at times as well and follows up with the slightly more general R^n case and the end also has some metric space content i think?

[gray gazelle]

Algebra:
Sets, Relations, and Functions

Complex Numbers and Quadratic Equations

Matrices and Determinants

Permutations and Combinations

Binomial Theorem and Its Applications

Sequences and Series

Calculus:
Limits, Continuity, and Differentiability

Differential Equations

Integral Calculus

Application of Derivatives

Application of Integrals

Coordinate Geometry:
Straight Lines

Conic Sections

Circles

Parabola

Ellipse

Hyperbola

Trigonometry:
Trigonometric Functions

Identities and Equations

Properties of Triangles

Inverse Trigonometric Functions

Vectors and 3D Geometry:
Vectors

Three-Dimensional Geometry

Probability and Statistics:
Probability

Statistics (mean, median, mode, standard deviation)

this is the portion

[molten gulch]

do not flood chat

[gray gazelle]

which is the best book for basic to advance mmath

[gray gazelle]

sorry

[rigid trail]

what this

[tender river]

the portion

[mortal granite]

Thank u

[mortal granite]

Mathematical analysis zorich-2

[wary jackal]

Do you guys know a book (pdf or digital copy) for algebra that goes from the basics to advance?

[proud osprey]

are you talking about school algebra or abstract algebra

[wary jackal]

School algebra

My foundation for algebra is kinda ehhh

[vital bane]

Khan Academy is great for that

[vast jackal]

aops intro to algebra really does a great job for it

or you can use khan academy like neamesis said

[normal crystal]

or openstax if you want it legit free
or any of a few standard textbooks that aren't

[remote sparrow]

springer publishes plenty of books in computer science

idk

[normal crystal]

there definitely are some
it's not like every springer math is a winner either

[main grove]

48 laws of power

W book

Useful

[remote vortex]

How has it been useful to you?

[remote sparrow]

https://www.youtube.com/watch?v=ez8hC76KMJ8

[main grove]

Communication with others

Like debating

Or just talking to someone you are not sure whether to trust or not

[molten gulch]

We've come to dislike most books in general and cast them off in favour of textbooks to satisfy all reading needs, no fiction, ofc

[mortal ore]

to prepare for a course in case you were allowed to skip content

or to prepare for research

or to look for information needed while youre actively researching

[silver stirrup]

just randomly wondering what people think about Hubbard's book on vector calculus

[mortal ore]

you should start looking into that

[silver stirrup]

"Vector Calculus, Linear Algebra, and Differential Forms: a unified approach"

[mortal ore]

doing research during undergrad only gets more and more important as the years go by

[molten gulch]

We like it, but as always, we recommend awaiting a wider variety of responses

[mortal ore]

ask an advisor in ur math department

[remote sparrow]

none if you're interested in a field of pure math

[mortal ore]

maybe theres an internal REU program you can apply to next year

[mortal ore]

what?

[remote sparrow]

best you can do is ask for a reading course

[naive lava]

++ ug research is one of the top things schools look for

highly unlikely, but if you manage to publish something not too bad in an actual journal as a single author

It'd probably put you over 4.0 gpa students

[solid grotto]

Hello, does anyone have access to Dummit & Foote in PDF version ? like a recent version ?

[molten gulch]

<@&268886789983436800> user seeks pirated materials

[sage python]

Unfortunately, by TOS we are not allowed to sanction distribution of pirated materials on here

[rigid trail]

Piracy is no party ahh 🏴‍☠️

[solid grotto]

Ok ok, sorry that I asked ...

[wary jackal]

Aight. Ty

[mortal ore]

<@&268886789983436800> ngl I don't think this should be here

This weird housing thing

[indigo blade]

I wonder if there’s a China MO 2021 book/e-book

Or others year

[alpine ridge]

Hello, can anyone recommend books about aerodynamics for someone who knows math but barely knows anything about physics

[proud osprey]

Any textbook recommendations on singular/cellular (co)homology via simplicial sets

[torpid prism]

gr

[teal tendon]

hey
How would i start preparing for international math modelling competition???

[marsh ingot]

Google it and you will find out eventually

[wraith cave]

beat me to it

[remote sparrow]

there's a pin with reviews of various books in algebraic topology

[proud osprey]

thanks I didn't see the pin

but I'm not sure if any of them are really what I'm looking for

my prof works very category theoretically with simplicial sets

[placid shuttle]

What is the best algebra book to prepare for calculus 1?

[marsh ingot]

?

[placid shuttle]

Im taking calculus 1 but i gotta learn algebra before taking it.

[vague kiln]

your best option is working through a precalclus textbook. it will cover all the essential topics to help you succeed in calc1 e.g. general algebra, logarithms, trigonometry, functions, etc.

i personally went straight to calculus so i cant speak to specific textbooks without a bit of guesswork -- a bit of googling, and trial and error, should help find a textbook thats right for you (look at google book previews or google "[book name] pdf" to see the quality

either that or khan acadmey / organic chem tutor (personally, i'd use khan academy and supplement it w videos from organic chem tutor when im confused, then find additional problems in a textbook, e.g. stewart's)

[proud osprey]

There was a crypto bot above my message

[marsh ingot]

Oh...

So odd seeing two bots so sudden

[pure cradle]

I personally like James Stewart's "Algebra & Trigonometry". But, Sullivan's "Algebra & Trigonometry" is good as well. Sullivan's textbook is more "beginner-friendly" compared to Stewart. In Stewart's textbook, some parts of the explanation are omitted because the author assumes that you have the background knowledge. However, in Sullivan's textbook, I think, he thoroughly explain things without assuming anything from the reader.

[pine pond]

guys i wanna lean maths

from basics high school math

to advance

which resources book can i follow

anyone

[pure osprey]

Hello

I'm new here

[pine pond]

hllo

[pure osprey]

I'm mod creator

[pine pond]

me too

ohh kk

[manic cairn]

then ask your professor!

side note:
if you’re learning alg top for the first time, just pick up any book you’ll actually work through.

[proud osprey]

his book recommendations are all in the pinned message

maybe I'll give tom Dieck a try

[wraith cave]

what level do you mean by advanced?

khan academy is good for basic math up to high school level

[fresh skiff]

Sour drop i lost the link you sent me (a red book on logic)

can you please resend it to me

[willow geyser]

any one read Proofs from THE BOOK?

[tender cobalt]

heard really good reviews about it. I read the first bits and it's quite nice. I don't know about learning proofs from it though.

[cold knot]

Which book I have to read to improve my Trigonometry

[remote sparrow]

https://www.logicmatters.net/tyl/

[cold knot]

Best book for ISI Maths Exam

[half void]

Very strange request but what’s a book that will get me to lie algebra cohomology

[graceful moon]

There may be better recomendations, I dont know the subject myself, but chapter 7 of Wiebel covers this, so theres at least an intro

[normal crystal]

[fresh skiff]

Aw thank you ^^

[willow geyser]

Yea I found a full pdf version of the book in an archive of mine

[muted shore]

Hello guys do you know any good engineering books before i enter college so i can master thos skills

[stuck zephyr]

depends on what engineering

[night granite]

I'm doing a course called mathematics methods and modelling and i'm currently only doing discrete equations but we arent working with a textbook - any recommendations

[green mirage]

Engineering mathematics by K.A. Stroud

But if you ask me I would avoid buying any textbook till you start classes

I'm doing the same course as a former classmate but in 2 different institutions. Same name and same ranking but they are not the same

[gray gazelle]

Best Calculus textbooks recommendations for high school students , please

[tender cobalt]

james stewart calculus or larson calculus

[naive lava]

what subject?

E&M? CM? QM?

[next gyro]

Thinking, Fast and Slow by Daniel Kahneman is in general a really good book.

[shadow kernel]

Yeah
Haven't gone deep into it but looks promising

[muted shore]

i see i have heard about that book

[muted shore]

i see still im wriitng my entrance exams and results will be back by next month so till then i have to wait but thanks for the advice

[vague kiln]

Thomas or Stewart: easy, intuitive, covers almost* everything well; exhaustive amounts of examples and practice questions. perfect for anyone studying anything stem related, and the prescriptive texts

*imo they’re both lacking in their explanations of epsilon-delta proofs but, unless you’re going into undergrad math, this is useless anyways

I found Spivak or Apostol too hard for when I first learnt calculus. Getting a bit of mathematical maturity and returning to these texts for a second course in calculus is how I would approach it

Supplementing any of these texts with youtube and online notes (e.g. Paul’s) is what I’d highly recommend — no matter what textbook you choose

[rose sphinx]

I've realize i'm not the best at math. Mainly in the areas of calculus, probability, trig and LA.

Are there any book recommendations for these?

[vernal mango]

yeah fr they just used the bounded condition to solve questions( i'm using thomas btw)

[naive lava]

spivak has a cm book

might be worth checking out

[native breach]

I see there’s a springer sale going on right now, any favorites that people would recommend?

[mellow wren]

Which sale?

[naive lava]

CM is pretty much completed 100 years ago lol

and that book is 15 years old or so

also, do you want something with manifolds? since you said ug CM i did't think of those stuff

ok that's on the math side

dw about it

for a first into, manifolds will be more than overkill

can you describe what you don't like in spivak so I can reccomend you something?

springer doesn't have many CM books afaik

[native breach]

The “Yellow Sale” advertised on their main site. I’m not sure if it’s a specific subset of books that’s on sale. It says up to 50% off, but I am unfamiliar with the majority of the titles that appear to actually be 50% off.

[naive lava]

okay than, in what aspects do you not like ug physics textbooks

like where do you want imorıveent?

what textbook are you using rn?

[graceful moon]

The springer website is unforgivably bad, i can genuinely never work out how to buy their books

This seems to be the list of books on sale: https://resource-cms.springernature.com/springer-cms/rest/v1/content/20141104/data/v5

[normal crystal]

Chipper wants to go from Mario Kart to Space Shuttle

[mortal ore]

Yo bro how's spongebob doing

[cunning elk]

ok but that's to be expected for 100 level physics

it's for people who:

• failed AP physics in high school
• just need to take it for their otherwise unrelated STEM degree
• etc

in which case sure they'll handwave the shit out of everything

[naive lava]

okay maybe you can try out something like taylor's CMi that's way better in terms of rigor but also has a lot more content so you have to pick and read

[remote sparrow]

you can look at marion and thornton too

[old elk]

I am compiling set theory for analysis and line algebra, do you recommend that I read the entire first chapter of Bourbaki's book and if not, what section of chapter 1 should I be aware of?

[old elk]

[half void]

I found this chapter on mit ocw and its super super helpful, thank you so much!!!

[half void]

I personally have my own stack and occasionally carry a few around when needed, but most of my stuff is pdfs on google drive

[zenith pelican]

The best book I read is 4 found dead

[vital bane]

mfw when I wanted to do research in CM

it's god's gift to this wonderful world

[naive lava]

I mean, you can, why not

my first paper was on CM

but you are not getting a job publishing CM papers

unless ur a mech eng ig

[tiny stone]

Hi I want to start learning real analysis, i am familiar with proofs(olympiad style problems) and calculus, but not any higher math, i wanted to use ocw, so should I use 18.100A or 18.100C

I just finished watching the first lecture of 18.100A, all of it was stuff i knew. Seeing the titles of the other lectures, i can confidently say I don't know those things, but since i found it quite easy, if i did 18.100C would it cover everything that's covered in 18.100A and be accessible even if i don't know higher math? That's my question more specifically

[remote sparrow]

in general, i'd avoid judging the difficulty of a course by its first lecture

[vital bane]

I will come up with Topological Lagrangian Field Theory in CM

[remote sparrow]

often the first lecture reviews stuff or goes over very basic notions, which means it's not representative of how difficult the course will be

[vital bane]

I think you can find info about the course and they will usually tell you what the prerequisties for the course are

especially in MIT OCW

[molten gulch]

You do not need bourbaki for this, most linear algebra and analysis texts will cover the set theory they expect you to know

[marsh ingot]

Not really, always on pdf. Its more comfortable unless I really like the book/author

[tiny stone]

okay, ill stick to 18.100A then, thanks!

[vernal mango]

Most of the time no coz pdf is available so

[teal tendon]

How would i start preparing for international math modelling competition???
I am in grade 11 rn need beginner book to make my foundation strong

[limber fern]

does anyone have a recommendation for optimization books
something with like "using matlab or python" or something

[cunning elk]

stop spamming the same question over and over, you’re only making it more likely for people to ignore you

[dry jacinth]

Hey I'm studying right now some Dijkstra guarded command language to prove the correctness of algorithms, and at some point the book I'm using right now motivates the idea of Hoare logic. Everything seems somewhat like discrete mathematics (Dijkstra uses weakest precondition which is based on a topic of discrete math AFAIK).

Do you have any book that could escalate up to the point of atleast grasping those deductive systems?, I tried some AI recommendations but most of them just mention stuff.

[old elk]

So I start with the algebra part of bourbaki?

[dry jacinth]

Also, I don't know if I can reformulate my question a little and post them on their respective channels, being more specific #theoretical-cs #proofs-and-logic and #discrete-math

Will that comply to the rules of the server?

[half void]

This is not true

Current research is just not what you would think it is

[naive lava]

well yea but i meant ug type CM

like for example P&S and Schwartz tell you very different things about renormalization

so that's why you might wanna prefer a newer book such as Schwarz

[vital bane]

what? people actually do research in classical mechanics these days? what kind of stuff is it?

[half void]

Well it depends on what you allow to fall under the scope of classical mechanics. Geometric mechanics is a good example

[vital bane]

seems like mathphys rather than physics

[teal tendon]

How would i start preparing for international math modelling competition???
I am in grade 11 rn need beginner book to make my foundation strong

[vital bane]

maybe people in competitive math channel will be able to help

[remote sparrow]

how are you accessing the unlisted videos?

where are you finding them

wait, i tried inspect element then clicked the element conveniently labeled "steady-paywall" and deleted it

is that how you did it?

[brave pebble]

hey what are some great books to understand set theory for a high-school graduate going into uni soon?

[vital bane]

@heady ember

[lapis parcel]

does anyone have the book 'Advanced Mathematica' by Jude Ndubuisi Onicha? I was thinking about getting it and wanted an opinion if it is worthwhile.

[heady ember]

Enderton's Elements of Set Theory provides a gentle intro to axiomatic set theory. If you have some familiarity with rigorous mathematics, then baby Jech might be suitable too.

Baby Jech: https://www.amazon.sg/Introduction-Set-Theory-Revised-Expanded/dp/0824779150

[vital bane]

Enderton introduces proofs?

[brave pebble]

thanks

[heady ember]

Yesn't? Idk what exactly you mean by "introduce proofs".

I just learnt to write proofs... by writing them --- trying to come up with sound arguments and writing them out in a coherent way.

[cinder sundial]

Can someone recommend me books for my first year b.tech mathematics ?

I kind of want not so much basic theory neither to less theory in book + there should qn practice qn in book

[vital bane]

Teaching you how to write proofs that is

[heady ember]

Yeah, well of course. But that's rather vague.

[vital bane]

Not really, it's the same as "teaching you set theory"

[normal crystal]

you're overthinking it
I did what I said
you showed me that CA 16 was paywalled
so I checked his website
went to the CA video list
clicked on the link he gave for 16
saw it was the newer posted video I linked

[heady ember]

Eh. Its like saying that you're teaching someone how to draw; there's a lot of variation as to how exactly you're teaching them drawing.

Its not like, say, teaching analysis, where at the core you have the relevant analysis theorems and the corresponding proofs --- possibly packaged with some nice structuring and exposition.

[remote sparrow]

https://thebrightsideofmathematics.com/courses/complex_analysis/overview/

was it this link?

[normal crystal]

I just used the top menu from the homepage
but yea, that takes you to the top of the list, scan down to 16
I don't get the Sign In reminder though, maybe because I have an adblocker

[remote sparrow]

i have ublock origin

but this doesn't get blocked

[normal crystal]

I'm on ipad safari, idk
does it really block you from seeing the rest of the page
or just an annoyance

[remote sparrow]

it does block me from seeing the rest of the page

actually even when i delete the steady-paywall line i only see the second vid and not the rest of them

i'm on pc atm

[normal crystal]

hmmm, strange
ok, so I tried to see on way back machine
and the Sign In appears there as I scan down but then disappeared
try it
https://web.archive.org/web/20250219114921/https://thebrightsideofmathematics.com/courses/complex_analysis/overview/

oops forget that, I thought it disappears but it doesn't

[zinc dagger]

for all I got to say here is Wings of Fire

[full cairn]

I was thinking of buying Dieudonne's History of Algebraic and Differential Topology, but it costs somewhere between 150 and 250 USD

Anyone have suggestions for other books that mix exposition with some historical context? Doesn't have to be a lot of history, I like Stillwell's Naive Lie Theory, where he just has a section at the end of each chapter where he gives a short overview of how and when things was developed

[graceful moon]

Not a recommendation, but I love when books do end a section with overviews, history and possibly further research and topics, huge fan of it. My noncom rings class had that, every time someone’s name came up they got a biography at the end of the chapter, and some discussion of where all these problems came from

[lunar breach]

easy

[remote sparrow]

@normal crystal looks like my method might be patched?

https://thebrightsideofmathematics.com/courses/measure_theory/overview/#part-10---lebesgues-dominated-convergence-theorem

if i try to go directly to the relevant page, then i only see the overview

probably should have just copied the link and had it downloaded instead of accessing the video directly through youtube

[normal crystal]

I don't know what you want me to see
but I can still access the video links, pdfs, quiz
maybe try another adblocker and/or different browser

[near eagle]

I have a professor that has research in functional data analysis and I am trying to understand his work and it requires operator theory. Any recommendations on resources for this? I am starting with building a base on bright side of mathematics videos as my background in functional analysis is weak.

I understand the basic ideas of functional analysis but not much past that

[remote sparrow]

ah, you wouldn't happen to be using a script blocker would you?

i just added noscript

now i can see every video

[normal crystal]

thankfully he's better at math than webdev🤡

[remote sparrow]

well actually steady has some guidelines for setting up a paywall

i got automodded for trying to post the help page link

but it does explicitly say that people can bypass the paywall by turning off javascript

• Despite having a hard JavaScript paywall, non-members can still access your content. A handful of people may take advantage of this, but in our experience it's not worth worrying about. Normally, members are motivated by wanting to support a publication rather than accessing exclusive content. As a publisher, you stand to gain more from putting your energy into your work and maintaining a good relationship with your community.

[normal crystal]

tbh though, I'm still confused why he would make one random video in a list paywalled then use a different posted version of the same video in the list on his website
I can't tell if it's intended or not

[remote sparrow]

i would assume it's to prevent people from double-paying for the same content

you can either access paywalled videos on youtube through youtube membership or you can get the videos from steady

[normal crystal]

hmm, maybe
I interpreted his site as saying the ad free versions were the perk
not that some videos on the main lists are restricted

[remote sparrow]

i mean he has a few other things like actual books that aren't so easily accessible

but i don't really care about those

his bread and butter has always been the videos

[normal crystal]

yea, the 3 books, the lecture pdfs, the quizzes, the ad free videos
those are the perks
I think some random extra videos maybe, not on a list
that's why I don't get the random videos being paywalled

[remote sparrow]

they could have been his most watched videos

barring the first few of a playlist

they're decent and they used to be free

[remote sparrow]

sometimes

[fresh skiff]

Yes

Oh wait no it is introductory

But not good for first course

[vital bane]

Oh damn that sounds like a sick book

One of my favorite math quotes is from him

There is hardly any theory which is more elementary [than linear algebra], in spite of the fact that generations of professors and textbook writers have obscured its simplicity by preposterous calculations with matrices.

Kind of

[tender cobalt]

~~i never took first course in LA, i started with Axler ~~

[remote vortex]

Next time I'm teaching a linear algebra course, I'm definitely going to steal "Preposterous calculations with matrices" as a chapter title.

[fresh skiff]

I mean mostly not good for the first course.

[foggy quest]

Whats wrong with calculations. I feel like learning how to calculate a Jordan decomposition enhances your understanding. You only need to do 2 to get a significant increase in understanding.

Even if the way you do by hand isn't state of the art, proving that the algorithm you did by hand is correct is a good exercise

[torpid prism]

Any recommendations on advanced number theory papers/books that aren't surveys or introductions?

[full cairn]

Agree! Did you follow a particular book in your noncom rings class?

[proud osprey]

Tu's Intro to Manifolds starts each section with a page or so of historical context

[full cairn]

Cool, thanks

[graceful moon]

They were notes written by the lecturer and her student, which was based on a course he did at Oxford which was based on an introduction to non commutative Noetherian rings by Goodearl and Warfield

[graceful moon]

So like vaguely based on that book, but I don’t think it has the history haha

[full cairn]

I see, thanks

[frozen terrace]

Can anyone suggest me a book for calculus and one for algebra? I have a basic understanding of both the concepts and am looking to get a deeper understanding.

[vital bane]

The point of the quote is not "computation bad" but rather emphasizing a purely computational approach to LA (or any field of math) is bad. Computation and intution should be balanced when presenting any material because they go hand in hand

[vital bane]

that's awesome

[native cradle]

Any nice ethnography suggestions chat?

[dry ridge]

Recommendation on godel's incompleteness theorem ?

[rain hound]

I used it for my first course and it worked great. But we’re all different. Can’t hurt to just pop it open and start reading. It’s available for free on Sheldon Axler’s (the author) website

If it doesn’t work for you. Another more applied and perhaps more accessible book is Linear Algebra Done Wrong by Treil. Also available for free on their website

[molten gulch]

Personally we also loved reading FIS, so that may also be your cup of tea

[fallow cypress]

it's marketed as a second semester book, but you could use it as a first introduction, it's more abstract than a typical first introduction though

[lavish radish]

Linear algebra done somewhat right

[gray gazelle]

any recommendation for those chaps book? pls

[rigid trail]

for which

[gray gazelle]

i had attache dthe portions

algebra ,calculus,trignometry,co ordinate geometry

[rigid trail]

khan academy

[gray gazelle]

book?

[rigid trail]

not worth it

just use free stuff

[gray gazelle]

kay

[humble spire]

Is aops precalc good for precalc or are there better options?

I did all of aops alg and geo

[remote sparrow]

like a textbook? or a pop introduction

[alpine tundra]

Anyone here read "Using the Borsuk-Ulam Theorem Lectures on Topological Methods in Combinatorics and Geometry"?

[stuck breach]

have you done the problems in this book? they're really hard, am i missing some prerequesites?