book-recommendations

[dry tangle]

alr. ty guys

[slow roost]

I recommend Tao and/or Pugh

[native cradle]

Too early for bartle?

It's not too hard

[slow roost]

Im not familiar with that

[native cradle]

Bartle and sherbert

Well, one thing

DON'T TOUCH RUDIN

[slow roost]

go ahead and have a look

it was my first analysis book

it’s challenging for sure and if I were teaching a first year analysis course it wouldn’t be my choice, but I think the amount of hate it gets is overblown

[wet sentinel]

yea i would say try it and decide what you want to do after that

[remote sparrow]

https://complexanalysis.org/

howell and mathews is good (now available for free online at the site linked)

brown and churchill is also good

for complex variables i mean

[remote sparrow]

<@&268886789983436800> scam

[long stratus]

what your fav book

[gray gazelle]

Any recommendations for self study calculus 1 book to build intuition ?not Stewart

[slow roost]

https://assets.openstax.org/oscms-prodcms/media/documents/Calculus_Volume_1_-_WEB_68M1Z5W.pdf

[gray gazelle]

Thanks

[pulsar veldt]

It depends if you have a good background

Stewart is recommended for people whose are starting out with math books

[gray gazelle]

@pulsar veldt looking for a book more for mathematicians then applied

[pulsar veldt]

Mathematicians are used to logic and abstraction

If so do you, people may recommend Apostol's, Spivak's or Courant's

[gray gazelle]

I see, thanks

[remote sparrow]

https://math.stackexchange.com/questions/4702510/difficulty-of-the-book-mathematical-logic-by-mileti

[icy temple]

Do y'all have any recommendations for Algebra and Trigonometry?

[gray gazelle]

Pre calculus by James Stewart is good

But really any book on algebra and trigonometry can do the job lmao

they all the same

Matter of fact if u just do khan academy vids that’s good enough and do some extra problem solving

You won’t even need a boo

[icy temple]

Thanks

[high rover]

Could anyone share or recommend resources for learning math from the very scratch? I want to truly understand what I'm doing. I've always wanted to know math in depth. I don't just want to get good grades, I want to learn! I want to learn enough to understand linear algebra and be able to apply it in graphical programming. Honestly, I only know the most basic: PEMDAS, and even then, I doubt I fully understand what I'm doing.

[mellow wren]

did you learn any algebra in high school?

[high rover]

No, I just half-know PEMDAS. I really wanna learn.

[celest furnace]

Do you mean more to start learning calculus?
I recommend I think its Calculus for the Practical Man by James E Thompson
Also the maths textsbooks by Bostock & Chandler, Pure Maths 2 and Further Maths) (they're technically for the old a-level syllabus but they are very good at explanations and they give lots of examples.

[high rover]

Thankies so much!! I will give it a look later. I'm so excited to finally understand maths =D!

[celest furnace]

Personally I find A level/Gcse books for getting you up to speed, the CGP ones are my favourite. Then for A level also, Bostock and Chandler, a bit old but

They are very good for learning maths.

[fossil garden]

I'll throw my hat in the ring for khan at this level too. As a second option I've been watching someone stream their "playthrough" of Foundations II on mathacademy.com and i think that resource is pretty decent.

[odd tendon]

Hello, any books recommended for mathematical history?

[slender dock]

Hi! I was looking for some sources to access some geometry problems to practice with.

[fossil garden]

Do you already have Chen's book?

[fossil garden]

I don't know how well-regarded Mathematics from the Birth of Numbers is by math historians— my parents had a copy that I haven't picked up for a long while. But from a naive reader's perspective I had a lot of fun with it

also sorry for ignoring you mq, i got distracted 😅
sure has! i kinda panicked in the spring lol but i exist again sometimes

[tough talon]

olympiad level?

[grim ore]

@fossil garden !!

Hey!

[midnight wedge]

hi guys

where should I go after khan academy? my target is to do a levels

[grim ore]

What are A-Level Topics (I am from the US)

[midnight wedge]

pure math, statistics, mechanics

Do you have any more to recommend or is that enough

[daring wolf]

geometric representation theory

[sacred thicket]

Opinion on alufi algebra chp0?

[old elk]

As with everything in life, if you already have experience in the field, it will be very useful.

I'm trying to finish my syllabus on group theory along with basic number theory. I hope to be there someday.

[molten gulch]

Pretty solid

[full cairn]

It's great, but not as a first intro to algebra. For a beginner text, you could consider Notes from the Underground

[warm sinew]

Everyone asks for what books y'all recommend to learn some math topic, but what books would you NOT recommend for its related topics?

(probably not very many but still, there might be one or two out there)

[full cairn]

Lie Groups by Duistermaat and Kolk sucks, it's ugly, and has literally no exposition. I don't know why I bought it

[warm sinew]

Probably this

[full cairn]

Another unrecommendation I have is Visual Complex Analysis, but that's not because it's bad, I think the visuals are great, but I just think learning complex analysis from a purely visual pov is way too hard compared to the traditional approach

[sacred thicket]

Imo non analysis parts of the book are the coolest ones. But yeah the geometric proofs/calculations of things like derivatives and integrals are very confusing

[full cairn]

The Lie groups course wasn't technically undergrad I guess, plus I got a C, so I clearly didn't do enough

It's the normal bachelor amount, uh 180 I think? 60 per year

I'm past my 3rd year, but I'm still in undergrad

I haven't done the full amount each semester, so I'll be done by christmas, or maybe I need one more course in the spring

Kinda, we get part stipend and part loan. And you can't be delayed more than a year, then you get no stipend

[slow roost]

nooo! I love this book so much. I recommend using it as a supplement to a more traditional book, but it’s so special and amazing for getting excited about the subject

[full cairn]

Yeah, I tried to use it as a main book for a while, and got a bit frustrated, but I'm sure it's better as a supplement

[slow roost]

understandable

[full cairn]

I really liked the explanation of complex differentiation, like how it's both scaling and rotation which makes it much stronger than real differentiation

I think he calls it "amplitwist", not sure how I feel about that term 🤔

[slow roost]

yeah, I can’t say Im a big fan of that term either, though he eventually settles on more standard terms I think. It has been a long time since I read it

[remote sparrow]

you probably saw the positive reviews for their multivariable analysis textbooks

[full cairn]

Lol, maybe

[full cairn]

What do you think of Visual Differential Geometry btw? Seems like it could have some nice insights, but it's huge and covers so much, so I don't wanna read it all

[slow roost]

I think it has some of the same issues as VCA in terms of not being a substitute for a traditional text to learn the subject rigorously by itself. But this subject is even more logical for such an approach, and I think the pictures and intuitive prose explanations for things are fantastic

I read it alongside Lee and Tu

[full cairn]

I see currently I would read it just for the diff forms, I haven't gotten to Riemannian manifolds yet

[hollow epoch]

Has anyone read Mileti's "Modern Mathematical Logic"? Any opinions on the text?

[remote sparrow]

https://math.stackexchange.com/questions/4702510/difficulty-of-the-book-mathematical-logic-by-mileti

https://www.logicmatters.net/tyl/booknotes/mileti-modern-mathematical-logic/

https://math.stackexchange.com/questions/4747011/seeking-a-rigorous-introduction-to-mathematical-logic-book-recommendation-neede

[remote sparrow]

@fallow cypress and @shut verge personally used draft copies of mileti

[fallow cypress]

I loved it

I personally felt like it was very clear to read, but this depends somewhat on your mathematical background; it might be worth reading another text like A Friendly Introduction to Mathematical Logic alongside it to see what you prefer

[hollow epoch]

@Sour Drop and I seem to be running the same roads these days. Thanks @mq and @fallow cypress logistERIC_regression

[fallow cypress]

it's funny that the answerers question the value of the induction chapter because I actually really enjoyed it

[hollow epoch]

Well, it is a first edition. I am sure that feedback will result in refinement.

[fallow cypress]

You'll definitely want a solid foundation in thinking about mathematical abstractions before reading Mileti's book, I think experience with abstract algebra is often helpful for this purpose even if it's not directly related to the content of the book

I would agree that Mileti's is a harder intro book for mathematical logic, but I find his arguments and exposition satisfyingly clean

[hollow epoch]

I think that I will give it a try. I have a master of applied mathematics. It's just that applied at my school apparently meant pick whatever courses you want on foundations as long as you focus on applications most of the time. I exited without even realizing at that age that I had not even been grounded in logic and set theory aside from the bits and pieces that needed to be introduced for the core course work.

[fallow cypress]

Enjoy! Mathematical logic is a wonderful field

[hollow epoch]

Thanks to all of you.

[remote sparrow]

#book-recommendations message

i'd say the book is worth it just for this pic alone

[fossil garden]

g'morning sri >.<

[old elk]

Long time no see, how are you?

[merry sphinx]

ayo pause

no

[remote sparrow]

https://sites.santafe.edu/~albers/teaching/dynamicsbooks.html

[remote sparrow]

@blissful shore what r u looking for in a book on logic

[sage kelp]

Has anyone had experience self-studying/using Advanced Calculus by Folland?

[sand pumice]

Hi everyone! 😁 I am currently reading Sipser's Introduction to the Theory of Computation. What are some good books for the next steps?

[molten gulch]

I've been eyeing arora and barak recently

(I'm a 4th year CS student, I've recently gotten into theoretical mathematics and been reading sipser and arora)

[sand pumice]

I also heard of that one! Does the content build upon Sipser, or are there gaps?

[molten gulch]

I believe if you've done the first half of the book or so it shouldn't be too hard to get into Arora

[sand pumice]

Oh, wonderful! Thank you!

[molten gulch]

Oh and there's a free prelim copy of the book available online legally

https://theory.cs.princeton.edu/complexity/book.pdf

[sand pumice]

Oh, wow, it's very kind of the authors to do so.

[remote sparrow]

there are a lot of errors in the official publication

i see the purported 4th printing has not fixed the errors noted in the review

[molten gulch]

Huh

wow

Good to know, thank you

Eventually wanting to do some AG probably, I'm also a fan of type theory, (some) logic, etc...

I also really enjoy algebra

I need to learn some analysis tho, I know basically none

I've been reading some of Cox Little and O'Shea's Ideals Varieties and Algorithms after it was recommended to me by spamakin and I've been enjoying it, though I'm very out of practice and haven't touched it since winter break because I got really busy

[deep badger]

Uh but there is logic and proofs thing which I’m not good at I mean I don’t know these

[remote sparrow]

https://www.youtube.com/watch?v=D-1V7HaWj3k

[remote sparrow]

https://www.amazon.com/Set-Theory-Cambridge-Mathematical-Textbooks/dp/1107120322

[remote sparrow]

you're probably more likely to get an informed response in #diff-geo-diff-top than here

[vital bane]

same

[heavy egret]

hi

[sacred thicket]

Its stated in the beginning of Lee riemannian and 13th chapter of Lee smooth. Basically first 12 chapters give most of the background needed (and it wouldn't hurt to read the 13th about Riemannian metric lol). But results of chapters 14, 16 and 19 are also mentioned as prereqs in the Lee riemannian.
P.S i haven't finished either book yet, so i dont know for sure

[dusky pasture]

Best books for algebra 2?

[gray gazelle]

Any book for group theory?
Beginner's level

[molten gulch]

What's your eventual goal? Depending on this the recommended book will be different

[cunning turtle]

https://www.amazon.com/Real-Analysis-Long-Form-Mathematics-Textbook/dp/1077254547 do you guys think this book is worth it?

[fathom verge]

What books do you guys recommend for A level maths or like Calculus

[molten gulch]

It's pretty good I've heard, probably comparable in difficulty to something like Abbott's analysis but that's all I know, you may want to wait for some more opinions too

[molten gulch]

Thomas' calculus was pretty okay when we read it for calculus 1 and 2 in uni

[restive pecan]

@fathom verge you may like this, but books are not necessarily easy tbh

[fathom verge]

What do you recommend

Online?

Resourves

[molten gulch]

<@&268886789983436800> pirated PDF

[restive pecan]

Huh?

[molten gulch]

That PDF is not legally available for free

[restive pecan]

You should have just asked me to delete it

[gray gazelle]

For immidiate purpose, college external exams

[molten gulch]

You cannot repost it

[restive pecan]

But i don't know 🤷

[fallow cypress]

We can't allow piracy on this server since it's against Discord TOS

[molten gulch]

#rules

[restive pecan]

I seriously didn't know

[restive pecan]

Noted

[fallow cypress]

You're not in trouble, I'm just telling you the rule

[restive pecan]

I see

[molten gulch]

Here are the steps we always follow FWIW:

• Check on the author's official university or other websites to see if they have a preprint available. If they do, link the WEBSITE and not the preprint or the direct PDF link so that others can verify for themselves that this is a legitimate preprint. (Also always check for errata pages).
• Check on Google to see whether the book shows up in Amazon or other retailers FEEL FREE TO SHARE THIS LINK.
• If there's no preprint, check what publisher the author uses, if it's Springer, CRC, etc... there's a chance that the book will be available via your university's library access. Check that. If it is, you may acquire a personal copy through these portals, many publishers have terms of service that copies acquired in this manner are for personal use and may not be distributed, so do not redistribute these copies online. If companies want to sue one day, it could go badly.
• If the book shows up on "random" websites as a PDF and the websites have odd or sketchy links, the text being available there means it's probably pirated and you should NOT link those websites to others on this server. PERSONAL USAGE OF THESE PAGES OR MATERIALS ON THESE PAGES IS AT YOUR OWN LEGAL AND PERSONAL RISK AND I AM NOT LIABLE FOR ANY ISSUES FACED (I am not advocating piracy with this statement)
• If you decide to pirate the text or acquire it off a previously pirated page, DO NOT REDISTRIBUTE IT HERE nor should you discuss the means by which you acquired the text. Piracy laws vary between countries and in some countries it is legal for someone to acquire pirated media for PERSONAL usage, though it is very patchy, if you do pirate texts at all, it is AT YOUR OWN RISK. Discord does NOT like when people pirate texts because under US law, it could get them in a LOT of trouble, so they pass down the burden to the users and especially in community servers, Discord is willing to make an example of this place because they have to.

[restive pecan]

Noted 💪

Thanks for the explanation

[dusky pasture]

Please

[molten gulch]

Algebra 2 as in highschool algebra or galois theory and rings?

[dusky pasture]

High school

I suck at it in school

[molten gulch]

https://www.stitz-zeager.com/Precalculus4.pdf Chapters 1-10 should cover most of what's done in alg

[dusky pasture]

So far polynomials in school

Im thinking of J. E. Thompson's book. Worth it?

I don't have much digital access, so books only for me

I've got a short attention span so physical books are best for me

[molten gulch]

Well that's on you

If you don't have a good study ethic, why should they trust you to use the unfiltered internet to study

[vast jackal]

any good number theory textbooks

elementary

not elementarically hard!

[molten gulch]

rosen

https://www.amazon.com/Elementary-Number-Theory-Its-Applications/dp/0201578891

[molten gulch]

Basic Mathematics by Serge Lang is also quite good https://www.amazon.com/Basic-Mathematics-Serge-Lang/dp/0387967877

[wicked fractal]

What's your level?

[vast jackal]

I've read it but it's not all number theory there to it

[vast jackal]

precalculus

a high school student

[wicked fractal]

I can recommend Silverman's "A friendly introduction to Number theory"

[molten gulch]

I did not respond to the one asking for number theory with this text

[vast jackal]

Also he fucked up explaining congruence modulo theorem to me

[vast jackal]

oh sorry

[wicked fractal]

If you want a sophisticated one you can try Ireland and Rosen

[vast jackal]

will it be super hard or just decent? I would like something balance

[wicked fractal]

Just try it

"High school student" level says nothing to me

[vast jackal]

modern number theory? by ireland and rosen?

[wicked fractal]

yes

[vast jackal]

but isn't the prerequisite of pure maths highschool math's?

[wicked fractal]

If that's too hard then stick with Silverman

[wicked fractal]

Prerequisites are using noggin

[molten gulch]

For chapters 1-11

Beyond that you should know the content of a first (and possibly) second undergraduate course in algebra

[wicked fractal]

Beyond that you should drop Ireland and pick Milne or Neukirch

[vast jackal]

I wonder if pure maths can be taken without doing any high school maths lol

[wicked fractal]

If you have done 0 proofs in high school that would be awkward

But it shouldn't be too bad

[vast jackal]

if a derivation of the quadratic formula is a proof then It's not awkward right?

[wicked fractal]

Just read the textbook and see if you can follow along

If not then switch to Silverman. It's way easier

[vast jackal]

what made you take mathematics as a major? and how would it feel for you if you're in a third world country where opportunities are scarce and you took mathematics?

• I'm really considering if I should either double major or the the other; I like mathematics foremost but I mean also wanted to explore the physics part where it's unfamiliar and out of my experiences in it especially when physics here is not treated very good due to lack of funds from the government

@wicked fractal wtf is this book man 😭

[molten gulch]

An introduction to number theory

[vast jackal]

for chapts 1-11

[molten gulch]

yes

[vast jackal]

I haven't read your image 😭

[vast jackal]

how do I get through the other pages?

[molten gulch]

what does this mean

[vast jackal]

after i finish 11

12-18

chapts

[wicked fractal]

You don't need to

[molten gulch]

To do chapters 12 and onwards? You need to know group theory and galois theory which is taught in any standard text on abstract algebra

But as Deltoid said, you're better off just reading Milne's notes instead

[wicked fractal]

These will be more advanced

[molten gulch]

https://www.jmilne.org/math/CourseNotes/

[wicked fractal]

Yes our lord and savior Milne will guide you through

[vast jackal]

can i learn pure maths without any calculus?

[wicked fractal]

You literally just need to use noggin

[molten gulch]

You must know some analysis

[vast jackal]

ain't no way pure maths is that easy

[wicked fractal]

If you're not familiar with proof techniques then look at that

[molten gulch]

No it's not, you do need to know a solid balance of analysis and algebra

[vast jackal]

abstract algebra or high school algebra?

[wicked fractal]

For elementary number theory you don't need to know residue theorem or Galois theory or whatever. It's fairly elementary

[molten gulch]

Take a guess

[vast jackal]

abstract

[wicked fractal]

Correct

[molten gulch]

I do because unless this shit's explained to me in terms of ring properties i just don't get it /hj

[wicked fractal]

That's the correct way to do it anyway

[vast jackal]

what are the prerequisites for analysis and algebra (abstract)

[molten gulch]

noggin

like unironically

just noggin

[vast jackal]

tf does noggin mean

[molten gulch]

"use your brain"

is what it means

[wicked fractal]

If you don't have the ability to use noggin it might be over

[molten gulch]

noggin is just a slang word for "brain" or "mind" or whatever

[vast jackal]

for analysis?

noggin also?

[molten gulch]

yes

baby rudin (principles of mathematical analysis) is the standard real analysis text, though if that seems a bit abstract and difficult, you can try abbott's understanding analysis

[vast jackal]

any good books so I can maximize my noggin mindfully for pure maths?

[wicked fractal]

cohomology of arithmetic groups is super nice as you go through math textbooks you'll get better at it

[wicked fractal]

What made you take mathematics as a major? Autism

[vernal mortar]

I just sent a list of my previous bans bro???

Banned for just a simple doc file...

Jk it was a zip bomb with quettabytes of just nothing

[molten gulch]

For analysis I've been reading abbott and zorich but I haven't touched either in several months so I'm not gonna comment

For linear algebra I really enjoyed friedberg insel and spence's linear algebra (4th edition, haven't read the 5th), and overall it's quite good. I also quite like Linear Algebra Done Wrong by Sergei Treil (available legally for free at https://www.math.brown.edu/streil/papers/LADW/LADW.html however there are a few issues (mainly in the chapter for diagonalization), there's also linear algebra done right by Sheldon Axler https://linear.axler.net/ however this book is one I personally didn't like much at all, and he also does everything very abstractly which may or may not be a bad thing, I wish he did a BIT more computation, but whatever, I refer back to it sometimes

For abstract algebra I quite like algebra by M. Artin and I've read some of it, though I really need to finish learning (introductory) group theory out of it at some point I tried to read a bit of Dummit and Foote for Algebra but I didn't like the chapter I read too much, heard it's got good exercises though

I'm also a fan of theory of computation and my favourite introduction to the subject is Introduction to the Theory of Computation by M. Sipser

[vernal mortar]

YOUNG FUCKING SHELDOOOOOOOOOOOOOON

[molten gulch]

<@&268886789983436800> low quality discussion and bringing up bans from another unrelated server for no reasn

[vernal mortar]

Well he didn't originate from young Sheldon but it would be boring if I just sheldon

God I missed an entire word

[wicked fractal]

[vast jackal]

thanks for such a wonderful recommendations and comments

[molten gulch]

Also, of-course remember to take everything I say with a grain of salt, my recommendations are highly opinionated and the books I like might not be books that you like

[pulsar veldt]

https://tenor.com/view/nerd-meme-funny-idk-cool-gif-15925381156197121154

[wet sentinel]

well i was in such a country and was about to start a math major there, the plan was to move to another country for masters/phd

but then i had to move to another country from bachelors

[wet sentinel]

i was worried ngl

bc it seems hard to get into a good uni for masters/phd if you were in some really unknown place etc..

at least those where my thoughts on the matter back then (i still have these thoughts rn too)

but i just went with what i liked the most

i cant tell you what you should or shouldnt do, but for me i didnt really care and said to myself that things will work out at the end if i do a good job in uni

also i would rather struggle to find a job in something i like rather than doing a job in something i hate

so idk what you should do, the most important thing is to not regret your choice later, choose and continue until then end. Dont give up midway

wait we are in #book-recommendations, i thought we were in #math-discussion

i mean logically speaking, it should be harder to get into a very good masters program too if you come from an unknown uni but i dont have any facts, its just what i think about the situation

ohhh i see, yea then it makes sense

[forest garden]

Guys .. could you recomend me some frensh math books .. i mean for algebra lvl ..if it s pdf it ll be better

[slow dawn]

Right now, I’m taking Multivariable calculus, and some of the problems I’m dealing with are geometric proofs using vectors. Here are some example problems:

Prove the diagonals of a parallelogram meet at right angles if and only if it’s a rhombus.

Show that the sum of the vectors from the midpoint of each side on a triangle to the
opposite vertices equals 0.

My issue isn’t the actual concept of vectors or vector operations (addition and subtraction), but actually approaching the proofs. Last time I did geometric proofs was freshman year geometry, but I don’t know if at this higher level of math there is a more general and formal approach/structure for proofs. Does anyone have any resources or suggestions for being able to tackle any sort of proof, because I’m looking ahead at the course content and we’ll be moving from geometric proofs to proofs relating to calculus formulas and concepts?

[normal crystal]

you want books in french but misspelled as "frensh"

[remote sparrow]

yeah

[forest garden]

Cmon.it s normal...

[normal crystal]

<@&268886789983436800>

[tender stag]

Can any of yall pls give me a good book, about mastering the basics of maths? Or generally speaking any book that i can use for second year of high-school

[normal crystal]

that can be different things for different people
you can use Openstax books or Khan Academy for basics up to HS

[real heath]

Long time ago, I personally used a few books by K.A. Stroud. There is one called "Foundation Mathematics" but they're kind of textbook price. ): On the up side, is available on Amazon so options to find used/other sellers. There's also "Engineering Mathematics" which also starts basic --> advanced. If I think of anything else, I will reply again ^^

[merry sphinx]

Maximize my noggin mindfully is a new phrase

[sand path]

Any recs for books on combinatorics ?

[molten gulch]

bona's walk through combinatorics

[crude sage]

Are there grad-level alternatives to the back half of Spivak's Calculus on Manifolds (i.e. integration on chains, differential forms, and so on)?

[daring wolf]

get a book on smooth manifolds
some books I know are lee’s one or tu’s one

[crude sage]

Very cool. Thanks

[gray gazelle]

I'm a highschool student and would like to learn more about pure mathematics (as it interests me) any book reccomendations?

[jagged wing]

Uh can you tell me what you think is pure? I have a lot of books in my list

[gray gazelle]

Maybe books with an introduction and another as further expansion or narrower part of that category, if it doesn't take you too much time then i wouldn't mind the full list either

[unkempt quartz]

I want to go into real analysis and currently searching for a beginner level book so ideally what would be a good start?

[remote sparrow]

#book-recommendations message

[remote sparrow]

@blissful shore bump

[blissful shore]

Oh woops i was supposed to reply but i think i just imagined i did instead of rly doing it. really i had lately been thinking about a video i saw ages ago in which the guy talked briefly about linear logic. so i want to learn more about logic systems such as that and others that might differ from it but are similar in that they are not classical logic. i basically want to get a feel for non classical logics in breadth even if that means sacrificing depth. ive been reading priest's Introduction to Non-Classical Logic a bit and that is along the lines of what im looking for

[remote sparrow]

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

i'm guessing u already looked thru this guide?

some books cover intuitionistic logic

u could ask in #foundations too

[jagged wing]

I did some research but I only found some deeply related with philosophy and physics if it’s ok

[gray gazelle]

sure /<3

[carmine trout]

hi, does someone have a solution file of "Linear Algebra Done Right" by Sheldon Axler ?

4th edition

[slow dawn]

Right now, I’m taking Multivariable calculus, and some of the problems I’m dealing with are geometric proofs using vectors. Here are some example problems:

Prove the diagonals of a parallelogram meet at right angles if and only if it’s a rhombus.

Show that the sum of the vectors from the midpoint of each side on a triangle to the
opposite vertices equals 0.

My issue isn’t the actual concept of vectors or vector operations (addition and subtraction), but actually approaching the proofs. Last time I did geometric proofs was freshman year geometry, but I don’t know if at this higher level of math there is a more general and formal approach/structure for proofs. Does anyone have any resources or suggestions for being able to tackle any sort of proof, because I’m looking ahead at the course content and we’ll be moving from geometric proofs to proofs relating to calculus formulas and concepts?

[cunning elk]

those are not particularly deep proofs beyond just definition recall

brush up on your basic plane geometry and you should be fine

[slow dawn]

Ok, thank you for the advice, I’ll try brushing up

[cunning elk]

that's how most proofs in lower level classes tend to go

just definition chase

[summer remnant]

I am currently doing course of khan academy linear algebra, and it is really making me invested and interested in it, but the problem is, It lacks subsequent questions to be more thorough with the concept, Does anyone know any good book or good website or any good resource, where i can solve the questions and view their subsequent solutions, I am looking forward to solve hard questions
Any help would be appreciated! Thanking you in anticipation.

[blissful shore]

thank you, ill take a look 💖

[verbal bolt]

I think I have a pdf of the answers
Dont rise your hopes high bc im not sure
I'll be home in about an hour so i might send later

[slow wadi]

Any books about olympiad math? I need a book that can explain it as simple as possible and also have training questions with solutions.
Appreciate it if there is

I especially need the books that covers geometry and combinatorics

[carmine trout]

okay thanks you

[verbal bolt]

here, found it:)

[carmine trout]

ohh

man

you making my day

thanks you

[verbal bolt]

im studying linearic as well rn, so if u want we can study together or ask me smth if u need help:)

[verbal bolt]

np

[carmine trout]

okay nice, i'll ask u if needed !!!

[gray gazelle]

aops books

they have a book on intro geo and intro/intermediate combinatorics

[slow wadi]

What is aops

[gray gazelle]

google is your friend

search it up you won't regret it

very positive experience with them when i was in hs

and apart from books they also have plenty of resources and a community for oly math

[slow wadi]

Art of Problem Solving?

Sure, will read it

[gray gazelle]

bingo

[gray gazelle]

LOL??!?!?!?

BRO

there is solution manual out there?

this is gonna be so darn helpful not even kidding

[verbal bolt]

Feels a godly feeling

[steel cloud]

What are the pre-requisites for alg geo?

[sage python]

Depends on how you approach it

If you do the more algebraic approach, then some basic point-set topology and some commutative algebra

And it might be nice to have seen cohomology in the setting of algebraic topology before sheaf cohomology

[crude sonnet]

chat is linear algebra by dr gilbert strang good?

[molten gulch]

Yes but I personally didn't like how concrete it was, I just prefer more abstract presentstions

[crude sonnet]

i mean, i just want a book for reference and learning, since its vaster than school level, i will be doing linear algebra to make a ai architech XD

[gray gazelle]

what level are you looking for

strang's book is very popular tbf

[crude sonnet]

idk really high level , since like i dont want anything to bottle neck and ruin optimization

[sage python]

And probably good to see some complex analysis and differential topology/geometry, since those inspire stuff in AG

If you're more complex AG, you wanna go much more into complex analysis and DG, becomes a hard necessity, while commutative algebra becomes a bit less important

[south magnet]

.

[steel cloud]

I don't know much about approaches, I am familiar with point set topology, not much but I know little bit commutative algebra

[dim phoenix]

Yo

[vast pecan]

Hi
Any recommended number theory books ? For a beginner

[molten gulch]

Rosen

[floral lantern]

If you want to learn about classical alg geo e.g curves read fulton’d book

It’ll teach you a lot of the basic comm alg

[daring wolf]

i mean there are several ways to get into that, like start with classical ag, scheme theory, complex algebraic geometry, etc.

for scheme theory, you'd need general topology and a bunch of commalg to get started
it's good to know what cohomologies are before doing cohomologies on schemes (like before harthorne ch. 3). Also it's good to know enough category theory

also backgrounds on smooth manifolds helps you very very much. This helps you understand why you define a geometric concept in that (ridiculous) way in the first place

[steel cloud]

Okay thank you

[fossil terrace]

I want to send out a recommendation for Mathematics for Human Flourishing by Francis Su (former MAA president). It’s such a joy of a book to read and very accessible for mathematicians of every level.

[vast pecan]

Thanks, but i don't think this is a beginner friendly book maybe?

[slender stump]

ok so i wanna ask yall if theres a book that i can read for uni since the material my prof gave me doesnt quite match what we are learning
im a first year in compsci and the "elementary mathematics" course covers functions, absolute values, linear equations, quadratic equations inequations etc
where could i find some kind of book (or multiple, I am willing to read more than one) that cover these and are relatively beginner friendly

[gray gazelle]

That sounds like pre calculus ish

Any pre calculus book would work

[slender stump]

do you got any recommendations?

like im down to read more than 1k pages

[gray gazelle]

Pre calculus by James Stewart

[slender stump]

tyy

[gray gazelle]

Got everything

[gray gazelle]

basic mathematics by serge lang (or undergrad algebra by serge lang. or algebra by serge lang if you're crazy)

[slender stump]

okay tyy
ima checkemout and prolly mix all the books i have so far to just ace the exams lmao

[molten gulch]

there's ireland and rosen which is not very beginner friendly (unless you're a maths major) but there's also "elementary number theory" by rosen which is more beginner friendly

[vast pecan]

I googled rosen number theory and first book was a graduate text , which made me wonder

[molten gulch]

Ireland and Rosen (that one) is also an introductory text

at-least the first 11 chapters are, they do assume a bit of group theory and calculus at parts but excluding that it covers basically everything in an elementary number theory course

it's a very common undergraduate book

The label "graduate texts in mathematics" is just a publishing mark by Springer

[vast pecan]

Thank you so much

[molten gulch]

But if that text scares you, I would still suggest rosen's friendly introduction

it does everything with a bit less abstractness and typical mathematics textbook denseness

[vast pecan]

Should i study discrete before this ?

Or any form of logic and proofs

[molten gulch]

here's how IR introduces unique factorization

[vast pecan]

Interesting

[molten gulch]

here's how rosen's introduction to NT handles it, as you can see, far more explanation and slower pacing

[molten gulch]

A PID is a principal ideal domain and a UFD is a unique factorization domain, for context

[true sail]

That's "A classical introduction to modern number theory"?

[molten gulch]

No, the first screenshot is

[molten gulch]

this one

[true sail]

And the second one?

[molten gulch]

Rosen's "Elementary Number Theory and Applications"

[true sail]

Thanks, I was thinking about Kenneth Rosen "discrete mathemathics and its applications", a totally different book

Thanks, I was thinking about Kenneth Rosen "discrete mathemathics and its applications", a totally different book

[molten gulch]

yes this is a very different book, but it is good if you want to learn some discrete mathematics, though to me discrete felt a lot like a smattering of topics you can learn better by reading a dedicated text on each

[true sail]

I see, thanks!

[warm cedar]

can anyone suggest hard books on extremal graph theory? i'm in high school so i don't know linear algebra or topology or whatever so it shouldn't need those it should do stuff elementarily and have fun nontrivial exercises
i also don't like the probabilistic method so ideally there wouldn't be too much of that

[molten gulch]

<@&268886789983436800> user is requesting pirated resources

[fallow cypress]

Sorry we can't allow piracy in this server

[junior heron]

So I have to buy that book for 80 dollars.. im a math student and not rich haha

[fallow cypress]

Are you currently at a uni? You might be able to find it at the uni library

Artin's book is pretty popular (if not, there might be other algebra books)

[junior heron]

yes I'm at uni but we can borrow only hard copies and I need it for the entire semester, so it's completely impractical. I actually just want to get the book bc of the exercises

[fallow cypress]

Ah I see

Weird, your uni doesn't have an ebook system?

I can't control what you do off the server, but unfortunately, if we allowed piracy here, we would violate the Discord TOS and be at risk of being shut down

[junior heron]

it does but its not trivial to navigate and I wanted to save time

[junior heron]

I get it

[deep moat]

A good mathbook that explains the "why" of each topic?
by mathbook I mean: like algebra, geometry, etc.

[vital bane]

"Why does Hahn decomposition work?"

"Because it is interesting"

[cunning elk]

proof by fucking obviousness

the aops intro series does a decent job motivating/proving the important results

even if not in full detail

[pulsar veldt]

Most of the books you see will have it

[marble bane]

Hello... i have Thomas' calculus and analytic geometry book with me, the way he explains multiple integrals is not good enough imo.

What other book do you suggest?

I don't want Apostol, something between both of them

[slow roost]

I like Colley - Vector Calculus

[marble bane]

Is it too verbose? Does it have solved examples?

[slow roost]

I don’t think it’s too verbose, and yeah it has lots of worked out examples, and solutions to all the exercises

or rather, solutions to the odd numbered exercises

[marble bane]

Cool

Unfortunately, colley isn't available in my nation

Thomas, Stewart, Apostol, Anton

Should I stick with Thomas or is there something better in this list?

@slow roost

[slow roost]

I've only read Stewart's single variable calculus book. I thought it was ok, nothing special

I haven't read the others there

you could check out some free options

like https://ocw.mit.edu/courses/res-18-001-calculus-fall-2023/pages/textbook/

or https://textbooks.aimath.org/textbooks/approved-textbooks/

[wintry quartz]

Im looking for a book that introduces cohomology and leads into the theory of topological invariants of vector bundles

Mainly I'm looking for something that will help me build up to understanding things like chern classes and the seift whitney classes

[slow roost]

Bott and Tu - Differential Forms in Algebraic Topology seems to be a classic for this

[wintry quartz]

I've heard that this book is rather dense, is this true?

[slow roost]

yeah, seems to be. I've barely tried to read it, I'm not ready yet

[wintry quartz]

I mean what even are the prereqs?

[slow roost]

I'm working on Tu's Differential Geometry book, which also introduces cohomology and vector bundle/characteristic class stuff

and it's much easier going (though still not easy, this stuff is just hard I think)

[wintry quartz]

wait lemme look at this

i'll be back in min

[wintry quartz]

I see that he does vector bundles and stuff, but doesn't seem to build up cohomology

but I guess his manifolds book is for that

[slow roost]

oh, I guess it's only de Rham cohomology

oh actually, you're right

that is the other book

[wintry quartz]

I looked up the word cohomology in the differential geometry book and I can see that he's using the knowledge of cohomology

and im guessing its not the deRham one

[slow roost]

I've been reading a bunch of Tu and Lee recently and I sometimes mix up what came from what

Lee's Smooth Manifolds book has de Rham cohomology but doesn't do much with vector bundles

[remote sparrow]

tu wrote An Introduction to Manifolds explicitly as a foundation for bott and tu

[slow roost]

I found this lecture series from him recently, from last year https://youtube.com/playlist?list=PLQZfZKhc0kiA149d8nmkY7DARwyjzHfl0&si=4tLK5GVhkU5etYkT

super cool

[orchid vortex]

Not related to what you’re discussing, but could you give a review of Tu’s (Smooth manifold and Differential geometry) and Lee’s books (Topological Manifolds and Smooth manifold)? Which one do you think is better for self-study?

[slow roost]

I think they're both really great. Tu's Manifolds book is roughly like a compressed version of Lee's Topological Manifolds and Smooth Manifolds, in one book. It doesn't cover quite as many topics as Lee's books, but all the main ones are there. Lee likes to painstakingly spell things out in the majority of his proofs and examples, and his books are resultingly quite a bit longer than Tu's. For example, Tu's Manifolds books has an Appendix A that covers point set topology for 20 pages. Pretty much the same material is chapters 2-4 of Lee's Topological Manifolds, which is about 100 pages. Topological Manifold's Appendix A on the other hand is a 15 page review of set theory, going as basic as the definitions of relation and function. So it really aims to be as self-contained as possible.

(Lee's Topological and Smooth Manifolds together are over 1100 pages, while Tu's Manifolds is 400, so Tu is really a lot more concise.)

Their Riemannian geometry books are somewhat more individual in content, though again the main topics are the same. Tu's is significantly more rapid paced, and gets to things Lee doesn't cover (characteristic classes) in 100 fewer pages. It starts out deceptively easy to follow but rapidly ramps up in difficulty. Lee kind of always feels like he's taking pains to hold your hand every step of the way. Some people find him overly wordy because of this, but it's my preference.

If I could only have one, I'd go with Lee. But I enjoy going back and forth between them

Oh, one very notable difference between them is, Tu's books actually have solutions to selected exercises, while Lee's have none

[grizzled oar]

Any recommendations for a first course ODE book that balances rigor and intuition (lots of examples, well-motivated)? Background: LADR + Analysis by Tao. Goal: dynamical systems/chaos.

[remote sparrow]

hirsch smale and devaney

can look at perko or arnold too

[tacit torrent]

Any good books on computer algebra(also symbolic computation in general) for self studying?

[orchid vortex]

Very helpful thank you so much👍

[lean badge]

hiii, does anyone have suggestions for algebra 1? seems to be mostly group theory

[molten gulch]

Artin

[lean badge]

ty!!

[molten gulch]

Dami also has a ton of algebra book reviews pinned, there's also GT specific books but many of those already assume an introductory algebra course ofc

[lean badge]

whats an introductory algebra course, my university seems to have group theory as "Algebra 1"

[molten gulch]

Mainly groups, yes

[gray gazelle]

if you can send the list of topics we could help with what specific book might be best

and yeah it’s mainly groups but sometimes you do some basic ring theory

[lean badge]

thanks!
subgroups, quotient groups, some rings, actions, orbit-stabilizer theorem, group representations, profinite groups, classical groups

[gray gazelle]

interesting

Can I also ask what your background is? I have two recommendations but one is far more gentle and the other assumes you have experience with proofs with sets and functions

[lean badge]

year 1 university student, doing discrete math
probably doing that class next year

[gray gazelle]

ah okay cool!

Then I wholeheartedly recommend “discovering group theory”

it is entirely self contained

if you want to learn more about proofs, I also recommend hammack “book of proof”

both are very pleasurable to read but not smooth sailing 100% so it will challenge you

[lean badge]

does it tend to be quite different? my discrete math course is entirely proof-based and i will have done a real analysis course by then <3

[gray gazelle]

ah

if you will have done analysis then you don’t need hammack

and honestly “discovering group theory” might even be underkill for you in that case

But if it is, then my second recommendation is either dummit and Foote or Pinter

I’d use Pinter for exposition and dummit for exercises

But part of reading math books is realising what you like and don’t so I will leave that to you

[lean badge]

ill check those out!

[mortal ore]

You'll likely use dummit and foote for algebra as its the standard

So its a good book to pick up once ur already familiar with group theory because a second go at algebra will help you refine ur introductory knowledge

[vital bane]

Dummit and Foote mentioned 🔥

It's so peak

[wicked fractal]

Dummit and shit (it's a good book)

[molten gulch]

Dummit and foote is nice but I feel a bit lost in the text everytime I try to read it

[molten gulch]

Have you seen the handbook of set theory 💀

[full cairn]

The ebook is even more expensive than the hardcover 💀

[gray gazelle]

OK but think of it as furniture tho

the absolute flex this would be on a coffee table

[outer helm]

yo guys do u have a good book on galois theory?

with proofs, exercices and answers if possible

[marble bane]

Hello, I want some online source material for integrals practice, easy and medium level

[marble bane]

An online collection of problems in pdf form, or perhaps as part of some course

I've been doing some problems from the online ncert class 12 pdf, on integrals

It has around 170 questions that are easy

[steep root]

Also do you guys have book recommendations for quantum mechanics and quantum physics stuff

[marble bane]

I have one

[molten gulch]

Don't many algebra texts cover galois theory? I think E. Artin also has a book on galois theory by itself, so does J. Milne

[marble bane]

Although it is OLD so nevermind

[wicked fractal]

Might be biased but if the author did some NT then their Galois book is usually great

E. Artin and Milne are great

[marble bane]

Sorry for pressing on, but do any of you have integral practice pdfs?

Not book excerpt pdfs but simple pdfs

[vital bane]

@muted nova Do you have this🗿

[muted nova]

Who do you think wrote it

[wicked fractal]

same energy

[full cairn]

Galois Theory by Cox is great, and for exercises I recommend Galois Theory Through Exercises

[outer helm]

alr i’ll see this thanks to all

[full cairn]

Milne has his notes on Galois theory available online: https://www.jmilne.org/math/CourseNotes/FT.pdf
They're good as a reference, but a bit succinct for a beginner imo

[muted nova]

In order to properly emulate nG, I’d need to not be lying through my teeth

[wicked fractal]

yeah milne assumes you know how to take etale cohomology when forced at gunpoint

[stark turret]

information geometry book reccs?

[floral lantern]

What perspective are you looking for?

A rigorous math treatment, a mathematically inclined treatment but not aiming to be rigorous, or a physics treatment?

[low wadi]

Does anyone know a good book that explains proofs. Like contradiction tions proof or induction easily

Like I want it to not only approach them mathematically

I don't know advanced math

[low wadi]

I'm doing computerscience

I need to be able to proof some problems with them

I won't proof math equations yet

The subject is called

Problem solving

[orchid otter]

Anyone know if Linear Algebra done right is ok to learn as a first linear algebra course? I’ve learned proofs

[orchid otter]

Get Richard hammacks book of proof

It gives all methods

[low wadi]

Ive seen a few books i don't want it to approach it from just a math prespective

Like too advanced

That I have to know some things prior

In my class we solve a puzzle for example using heuristics and then we prove what we found out

Without any complex math

[low wadi]

I'll look into it tho

Thanks

[orchid otter]

The one I said is really simple, all you need is high school math

[low wadi]

Alright thank you man

[molten gulch]

Hammack or velleman are good, hammack is free

[low wadi]

thanks

should i also read the fundementals? or just go directly to the proof i need

?

what do u suggest

i dont wanna get confused

[orchid otter]

Read the first chapter on set theory

[low wadi]

im asking this because my prof told me that i shouldnt read books on proof bc they will get me more confused about the subject

[orchid otter]

And there’s another chapter on some number theory, you should read that to learn combinatoric proof

[low wadi]

alright

[low wadi]

okay thank you

[orchid otter]

Yeah, no problem.

[remote sparrow]

shahriari. pinter is good for motivation

[remote sparrow]

it's probably the gentlest second pass

[orchid otter]

Is Pinters good for abstract algebra?

[slow roost]

Pinter is lovely

[orchid otter]

Nice, I was thinking of using it as a first course in abstract algebra.

[slow roost]

I think it’s a great choice, very accessible, lots of pictures/diagrams for an algebra book, and it has solutions to some selected exercises

[orchid otter]

Perfect, thanks.

[normal crystal]

do you have any opinion on Shahriari's Combinatorics book?

[remote sparrow]

no

[molten gulch]

Does this course have linear algebra as a prerequisite?

[normal crystal]

I can't tell sometimes if you are a real potato or a character in an 80s/90s movie

https://tenor.com/view/potato-laugh-kepala-ubi-gif-1769729172946268170

[pure jackal]

Set theory, starting at introductory. I'm currently in multivariable calculus but I've also done a bit of linear algebra and differential equations independently.

[pure jackal]

Also a book on how to recover from visual trauma.

[molten gulch]

butterfly? zassenhaus lemma reference?

[wicked fractal]

the guy she told you not to worry about:

[remote sparrow]

the early material on groups is a bit densely written and could use more motivation for a complete beginner.

[royal mica]

Anyone knows a book that I can use for the base of my Olympiad learning?

[glass creek]

Would “the rising sea” by Vakil be a good alternative to Hartshorne?

[regal cloud]

well depends on what type of math competition it is i myself am studying for one but if its just in general then i think mathematical olympiad challenges is a nice book for youre need hope this helps sincerely Arthur

[crystal estuary]

Math

[daring wolf]

It is overall good but I don't like it because this is too long and gets boring

the real stuffs from hartshorne is like about ~200 pages (Ch2-Ch3) but you need to read much much stupidly longer texts in vakil

[dim delta]

Does anyone have any experience with structural induction in mathematical logic? I’m currently working through enderton’s mathematical introduction to logic and I’d like a book that gives a more gentle explanation of induction. Anyone have any suggestions?

[molten gulch]

I've heard it's good, is quite a bit longer due to covering stuff slower

[native cradle]

Any books exploring mostly finite dim LA , with a flavour of infinite dim vector spaces?

[tender river]

roman, greub, brown

roman and greub here -
#book-recommendations message
brown - https://www.amazon.com/Second-Course-Linear-Algebra/dp/0471626023

[native cradle]

tq

[foggy quest]

The flavor of finite dimensional (linear algebra) and infinite dimensional vector spaces (functional analysis) is very different.

[red quiver]

any books for pnc?

[molten gulch]

What is PNC

[red quiver]

permutations and combinations

[molten gulch]

Rosen's discrete mathematics

[red quiver]

is it like a problems book or conceptual

[molten gulch]

It's a textbook

It has a chapter on basic combinatorics that should cover permutations and combinations

If you're interested in further combinatorics look into Bona's A Walk Through Combinatorics

[red quiver]

thanks gng

[molten gulch]

Does anyone have any resources that describe the Church Turing thesis, lambda calculus, computable functions, combinators, and similar? I've had one course in theory of computation at uni but we did not cover lambda calculus and I'd wanted to learn a bit about it. Videos, books, expository papers, anything is fine

(If anyone has suggestions please ping on reply)

[vital bane]

@solemn pilot It's time for your CS nature to shine

[native cradle]

I know

but the thing is my course does stuff on hamel basis

and usualy examines how basic properties work in infiniet dims

[vital bane]

Most things don't work in infinite dimensions right? Because almost everything we do in linear algebra requires an ordered basis

Like determinant for example

So we need a whole new theory

[sacred thicket]

-# if only there was a book that goes through most of linear algebra without using discriminants

[vital bane]

If only that book could describe a way to actually compute eigenvalues...

[molten gulch]

he does in a slightly bleak way

[vital bane]

[native cradle]

fair enough

Lemme continue working on my assignment in that case

will probably learn a lot from these actually new problems

[native cradle]

also

[vital bane]

alos

[native cradle]

hi , haven't seen you around in a while

[vital bane]

I haven't even seen myself in a while

and yes, hello 👋

[vital bane]

Don't let me stop you, but yeah there are books that try to do as many things as possible in an arbitrary vector space regardless of dimension

mostly algebraic books

and my LA prof

[molten gulch]

lang (algebra)?

[native cradle]

my 500 lvl course 😔 too

My RA prof scolded me for taking operator theory ( a 500 lvl cours)(

[molten gulch]

Why?

[native cradle]

too early he said

and I've taken on too much this sem

[vital bane]

Well yeah, don't you need to know functional analysis to learn operator theory

[native cradle]

It's just finite dim LA here

with basic operators being studied

[vital bane]

finite dim LA course is called "operator theory"?

[native cradle]

i'll share the syllabus

[molten gulch]

[vital bane]

Hopefully I will know more than I do now

[molten gulch]

This reads like a theoretical LA course with some spectral theory

[hasty trellis]

Hiiii,Are there any books or materials in general writing about finding closed form of some types of sums,that I can get recommendations on

thanks in advance

[vital bane]

by sums you mean infinite series or finite sums?

[hasty trellis]

Finite one, but both is okay

[native cradle]

that susms it up

[molten gulch]

Finding the value of finite sums just turns into writing out the sum and either summing by hand or using a calculator

Infinite sums are...a bit more interesting to my understanding

[native cradle]

At times finite sums have nice "tricks"

[molten gulch]

ye such as geometric sums

[native cradle]

$\sum_{n=1}^{m} \frac{1}{n(n+1)}$

[hasty eagle]

wai

[hasty trellis]

Yeah I want to know how to simply sum like how we do with telescope sum

[vital bane]

Yeah but the point of a closed form is to avoid writing out the sum and adding up individual terms Like how \sum_1^n k is just n(n + 1)/2

[hasty trellis]

But like more type of sum and method and not just telescope one or maybe telescope one but more advanced idk

[vital bane]

I guess you could check out this https://youtu.be/8L2mAB_dwNs (the first result I got from google)

[native cradle]

The thing is being taught by a functional analyst means she tries to give us a feel of what infinite dim vs look like

for which most books have next to no problems

[vital bane]

my condolences

My LA course is being taught by an operator theorist

[native cradle]

I mean we literally asked for it

[vital bane]

he spent 3 weeks doing category theory

to define direct sum and tensor products of vector spaces

tbh I should've paid attention and gone back and reviewed what he taught back then now I regret it

[native cradle]

Same here

Historically this course used to be taught by my current RA prof

this man has literally taught every single course at some point

[vital bane]

based

[native cradle]

Algebra, number theory, probability, RA, operator theory, LA

[vital bane]

I aspire to be like that

[tame tree]

because its well within the realm of “functional analysis”

the things you can say about inf dim without more analysis or topology is very limited

axler does have problems involving inf dim

[native cradle]

that's another thing, I want to do a reading project on FA next year

[tame tree]

but theyre very boring imo

[native cradle]

I remember proving every LT has a poly such that p(T)=0

that was fun

[next surge]

Guys do you have some recommendations to prepare for IMC?

[median edge]

Is there some sort of "comprehensive collection of somewhat famous/ classical math probs" which includes stuff like oddtown eventown and all?

[remote sparrow]

https://www.amazon.com/Lambda-Calculus-Combinators-Introduction-Roger-Hindley/dp/0521898854

[molten gulch]

oh shit 👀 this looks really nice

[remote sparrow]

https://www.amazon.com/Type-Theory-Formal-Proof-Introduction/dp/110703650X

https://www.amazon.com/Computability-Theory-Chapman-Hall-Mathematics/dp/1584882379

[molten gulch]

Thank you sourdrop :)

[remote sparrow]

[molten gulch]

[languid bloom]

depends on the book as some require much more attention than others

[molten gulch]

Depends

[rigid trail]

This book is goated

[hasty linden]

Why ?

[rigid trail]

Very detailed and clear presentation of type theory

it's better than other books I've looked at which are more confusing

[hasty linden]

I think this book is not for me
Right now maybe if I take ai then I will think 🤔

[rigid trail]

It's for you if you want to learn type theory, otherwise it's not for you

[hasty linden]

But currently I m in 10th 🤣

[molten gulch]

Grade doesn't matter, either you have the prerequisites or you don't, and if you do you can read the text

[rigid trail]

There are technically no prerequisites for that book

But it gets somewhat difficult so "mathematical maturity" is necessary

[hasty linden]

Thanks guys I will check it out now

[remote sparrow]

never heard of any

[heady ember]

Cambridge might not have discounts but sailiing the seven seas is always on 100% discount, excluding utility bills and the cost of owning a internet-capable device.

[remote sparrow]

i don't ever check hashes, but i thought they included hashes

[grim halo]

hi is there a good roadmap with books 🥒 (ignore the cucumber)

[hasty trellis]

Hiii, are there any book about calculus that focus on the exercises, like a workbook that I can get recommendations on ( calc 1-2)

If there're any workbooks focus on integral and application in finding volumes and area that would be great

Thank in advance

[remote sparrow]

https://www.amazon.com/Essential-Calculus-Practice-Workbook-Solutions/dp/1941691242

there's also one for calc 3 should you decide to study that in the future

https://www.amazon.com/Calculus-Multiple-Variables-Essential-Workbook/dp/1941691374

[gray gazelle]

I second these two recs by Sour Drop, they were very useful when I was studying calculus

[muted acorn]

can someone suggest a book on distribution theory for M1 and M2?

[foggy quest]

what is M1 and M2?

[foggy quest]

Do you mean distribution theory as in PDE or as in probability

[gray gazelle]

hi

any good linear algebra book i can use for reference

with the axler

i will check it out thanks!!!

[molten gulch]

meow

[molten gulch]

FIS is really good, we like it a lot, there's also werner greub which is far more encyclopaedic of the bits I've read -Ryan

at this point just ping me whenever you want to recommend FIS smh smh smh

There's also Hoffman and Kunze, which some of our friends at uni shill to us, yet we haven't tried it yet

[molten gulch]

I wouldn't expect any different somehow?

Like, why the hell are we manga-fying mathematics

[normal crystal]

that series is older and using manga for instruction isn't that unusual there

[true sail]

Memes to drive curiosity

[foggy quest]

Introduction to Analysis in Several Variables here maybe: https://mtaylor.web.unc.edu/notes/math-521-522-basic-undergraduate-analysis-advanced-calculus/.

[mortal ore]

honestly growing up with minecraft was awesome so i cant agree

i suppose but the existence of orbits and stabilizers rely on group actions existing prior

im not immediately thinking of another major result but i do know that group actions just offer a seriously good perspective on group theory

especially considering how early one can reasonably learn about them

[sage python]

Wait are you asking what are some applications of group actions?

[mortal ore]

nah this is a follow-up about a discussion we had a few days ago where i thought it was strange how so many algebra textbooks put off group actions

not just strange but i thought it was a bad thing

and currently still do

[sage python]

Oh yeah I don't like that choice at all

Group actions are almost the point of group theory

[mortal ore]

ive taken (or i suppose im still taking the second) two algebra 1 courses, the first had barely any group actions, the second involves them as a central topic

[sage python]

But I meant this question in particular

[mortal ore]

and having group actions just makes everything so much more beautiful

and opens a lot of doors

[mortal ore]

one of the arguments i gave for having group actions much earlier was "they are used in many theorems that are seen in introductory group theory"

[sage python]

Okay so that's what we're looking for examples of, then

[mortal ore]

many proofs of theorems i should say

[sage python]

Since "useful for group actions" sounds like used in the theory of group actions

In which case orbit-stabilizer is definitely the big one

But as far as applications of group actions, you want something external

[mortal ore]

sylow theorems are a good one

[sage python]

Actually let me advocate for this paper real quick

No it's an expo paper

Expository

[slow roost]

Pressley, Elementary Differential Geometry

[slow roost]

the whole notion that groups have to do with "symmetries" of things relies on group actions. It is how they were first studied. So yeah, I agree

[foggy quest]

yeah it covers differential geometry, but it's terse

[slow roost]

it doesn't look like that does cover differential geometry - seems to be a multivariable calculus course. That is a prerequisite to diff geo, though

ah, I see there is some mention of curvature and torsion in there

[ripe lance]

Some book recommendations (late high school or early college level) on combinatorics, probability, and mathematical reasoning and logic?

And perhaps some book OR non book resources on complex numbers and argand plane manipulation

[slow roost]

Needham, Visual Complex Analysis

(for the latter)

for the former, if the focus is on mathematical reasoning and logic, there's Gowers, Mathematics: A Very Short Introduction

combinatorics and probability will usually be their own books

[molten gulch]

bona's walk through combinatorics
stein and shakarchi complex anlaysis or freitag and busam complex analysis (assuming you know real analysis)
for reasoning you have a proof book like hammack or velleman

[remote sparrow]

https://complexanalysis.org

see chapter 1

depends on the book

sometimes all you need is the standard calculus sequence

[foggy quest]

it is for sure a prerequisite

[normal crystal]

that's basically a discrete math text like Epp or Rosen

[ripe lance]

Thanks, ill check this out and some if the other complex analysis books suggested

I think real analysis, linear algebra(upto atleast 2x2 matrix), series and sequences, calc are pre-requisites for complex analysis

[ripe lance]

Ill see into bona’s thank you so much!

[unique pier]

any real-analysis sources recommend?

[molten gulch]

Abbott is good for a nice intro, Rudin is standard, there's also Pugh, Bartle, Amann and Escher, Zorich, etc... if Abbott or Rudin aren't quite your style

[unique pier]

alr thx

[velvet flax]

dieudonne

[tranquil saffron]

Hello, everyone!

What are some book recommendations for AMC10? I aim to make USAJMO this year but have my 8th grade (next year), my 9th grade, and my 10th grade years.

I use all books on the AOPS Book Store, handouts, AMC books, formula books, and other resources found on https://mathematics.gg/books.

[radiant marlin]

hows MIRA as a first measure theory book, as opposed to a multivariate measure theory book?

[remote sparrow]

multivariate measure theory?

[radiant marlin]

measure theory on R^n instead of R which is what Axler does in MIRA

pls correct me if i am using a wrong /non standard term

[vital chasm]

I'm not sure there's much differences working on measures in R as opposed to R^n

For an introductory course at least

Unless youre dealing with borel measures on the real line and BV functions

[vital bane]

I don't think any measure theory book does measure theory only on R

that would defeat the point of measure theory

It's like talking about metric spaces but restricting yourself to only R with different metrics

[vital bane]

Axler definitely does not do measure theory on just R lol

He defines measures on a general measurable space

PEAK!

[heady ember]

Akm AsKuaLLY its bAd TyPogRaPhY to hAve dIffERENT fonT sIzeS iN oNe DoCumENT.

[remote sparrow]

https://www.youtube.com/@TheMathSorcerer/videos

bro's thumbnails and titles are getting more unhinged every day

the falloff is wild

[woeful terrace]

Wild

Did you see the books he sells

He sells what’s probably AI generated slop

[tulip sparrow]

Yo

Can y'all recommend a book for olympiad geometry?

1 stage less harder than IMO lv

[remote sparrow]

that's his newer stuff

i liked when he just stuck to book reviews and problem-solving

some of his old problem-solving vids helped me

[remote sparrow]

it is

[vital bane]

What does bro mean by "almost"??

FTFY

[pastel atlas]

Best book for starting linear algebra? Like from scratch, not even knowing what a Vector is

[distant prism]

saelina

[pine tundra]

https://youtu.be/5MXrNU6XH8I?si=sjIR6imFJvZvcJ2O

[remote sparrow]

this dude is pretty cool

he did a phd in physics @vital bane

[vital bane]

Yea I did

[remote sparrow]

https://tenor.com/view/cirno-cirno-fumo-fumo-touhou-fumo-plush-fumo-gif-25572816

[vital bane]

Touhou?

Sour drop ruined by Deltoid 😔

[trim summit]

Why do you have so many roles

[vital bane]

Pretty cool

[vital bane]

Because he's a role model🗿

[trim summit]

🙏

[remote sparrow]

i've been talking about fumos on here way before @wicked fractal

[trim summit]

How to be smart

[vital bane]

Develop discipline

[trim summit]

How can i do that when i wake up in the evening and sleep at 4am

[vital bane]

Try fixing that first

[trim summit]

Whenever i try studi my mind rejects me

[trim summit]

I will frfr

[vital bane]

One step at a time, go to sleep at 3 am for a week

[remote sparrow]

if your sleep schedule is consistent and it aligns with other priorities and responsibilities, i see no problem with being a night owl

[vital bane]

then 2 am the next week

then 1 am the week after that

[vital bane]

This is true

consistency is more important

but I prefer not being a night owl

[trim summit]

Thats true ig

I normally study at late hours

Cus thats the only time my mind lets me

[vital bane]

But do you get 8 hours of sleep?

[trim summit]

Mostly yes

[remote sparrow]

#study-discussion

[vital bane]

Sour drop, you should start a youtube channel like this

reviewing books

[remote sparrow]

perhaps

https://tenor.com/view/shion-fumo-yorigami-shion-yorigami-beanie-gif-23589732

[radiant marlin]

fair ig but he mostly looks as X as subsets R, in theorems and exercises. I suppose generalizations are obvious so doing it on R may actually be cleaner

[molten gulch]

Friedberg or Hoffman

[radiant marlin]

MIRA is a good book tho fr

[woeful terrace]

dummit and foote

evans

artin

no js evans

rlly
ik someone who thinks artin isnt that good

but they like dummit and foote

kunen

[sterile horizon]

Someone say my name?

[sterile horizon]

Oh, no

[wicked fractal]

Fumo fumo

[tender stag]

Yo anyone knows an exceptional book about functions that has everything about them, from basics, to expert things pls pls pls?

[wet sentinel]

there is nothing like that

what i mean is that this request is vague

so for example to study things like continuity, differentiability etc... then you pick an intro real analysis book. To study homomorphisms (functions with certain properties) and things related you go for algebra etc...

so there is nothing like a "book that has everything about functions" whatever that means

[rigid trail]

about functions?

What about functions

[tender stag]

Yes like everything if possible, I want to rebuild basics

[rigid trail]

What subset of everything because i'm sure you don't mean everything

[tender stag]

Let's everything until the level of a senior high-schooler

[rigid trail]

if you truly know EVERYTHING about functions/mappings then you know all of mathematics basically

[rigid trail]

Then you probably don't need a book

[echo elm]

Precalc?

[tender stag]

Yeah forgot that after a certain point everything is related to them

[rigid trail]

Some concepts to review: domain, range, codomain, injective, surjective, bijective

[tender stag]

Yeah

[rigid trail]

i think this is all you rlly need to know

but i'm not sure what your curriculum is

[echo elm]

Maybe this helps

[tender stag]

Yeah these and what do we call f○g for example

[rigid trail]

composition

[echo elm]

Thanks to pika he sent me this

[rigid trail]

inverses

[tender stag]

Thanks G appreciate the help

[echo elm]

No prob , glad I could help

[tender stag]

Yeah these types of functions and their graphs and everything sandwiched in between them

[rigid trail]

so domain, range, injection, surjection, bijection, inverse, composition

just review those concepts

[echo elm]

By the way which field of math that studies relations like the ones you mentioned?
I haven’t studied it in high school in that depth

[tender stag]

Thanks Gang, but do you have like a good book for each of them (I am asking for a lat sorry 🙂 l)

[rigid trail]

it's high school math

[rigid trail]

You do not need books

it's just a couple of concepts

[rigid trail]

technically part of set theory

[tender stag]

But those concepts can get deep tho

[echo elm]

Thanks ,that’s what I’m looking for

[rigid trail]

For high school you're chilling

you don't need to know all that much about functions besides those fundamental concepts

a book is way way overkill

[tender stag]

Bruh I am not in America so it may differ this is way I want to be safe rather then sorry

[rigid trail]

it's still high school level though right

[tender stag]

Yeah

[rigid trail]

they should only be teaching concepts like these

you can learn them all in a day

[tender stag]

Ok thanks I will continue my research, thanks a lot appreciate you for the time you have given me

[echo elm]

If you want deep ,then watch (bright side of mathematics ) although I wouldn’t recommend for high school level rather for college maybe

[tender stag]

Some extra knowledge wouldn't hurt right?

[echo elm]

Exactly

[leaden rapids]

Can anyone recommend a book on chaos theory and dynamic nonlinear systems? Something beginner friendly, I want to use it for a school project

[molten gulch]

Strogatz and devaney are standard introductions to dynamical systems and ODE to my understanding

[pulsar veldt]

Pre Calculus by S. Axler

Skiping section 0

[west comet]

I don’t like repeating mathematics

I only need trigonometry probably or geometry or I really don’t know

[tranquil saffron]

Help gng

[tranquil saffron]

Id appreciate this.

@west comet how useful was the book

[west comet]

You don’t need my book for amc10 atleast

[tranquil saffron]

THis book

[west comet]

Just do aops

[tranquil saffron]

I do Aops Wiki AMC10, Math Jams, and classes. I have all the books and studying htem too.

[tranquil saffron]

aight

[west comet]

Yea well finish them

That’s the only thing

[tranquil saffron]

aight

did u take AMC10?

[west comet]

You need for theory

[west comet]

Im not from the US but I researched alot

Read evan chen’s advice

[tranquil saffron]

Where are u from, if ur ok mentioning.

[tranquil saffron]

ok

[tranquil saffron]

Where is this webpage w/ advice, @west comet

[west comet]

Search “evan chen advice”

Khan only gives approaches no theory

[molten gulch]

Use google

[normal crystal]

but how do I find google
forget it, I'll google it🤡

[valid narwhal]

Hi i was wondering if there were some university who puts their undergraduate courses (detailed notes or lecture videos) online for free and have great amounts of complementary problem sheets with it so i can self study the typical undergrad math curriculum

[sacred thicket]

Independed moscow university posts everything online and is super good.
though unless you know russian, it wont be useful unfortunately

[hybrid sigil]

You can find quite a lot of lecture notes and problem sheets from Oxford: https://courses.maths.ox.ac.uk/course/index.php?categoryid=876

they are split into four years (Prelims, Part A, B, C), each has three trimesters (Michaelmas, Hilary, Trinity). You can expland and click on the course that interest you. There are no videos though, but many courses have lecture notes, reading lists and sometimes problem sheets.

[valid narwhal]

Wow that is much more structured than mit, might use that one

Thanks ever so much

[hybrid sigil]

they also have course synopses, so that you can figure out dependencies between courses. A list of PDFs here: https://courses.maths.ox.ac.uk/mod/folder/view.php?id=55865#50879

[west comet]

Hey bro can you recommend me some books on algebra and trig?

[hybrid sigil]

Cambridge also has a similar repository of lecture notes for undergraduate maths. Also, there are past exams papers. Here: https://www.maths.cam.ac.uk/undergrad/studentreps/tripos-specific-resources

[torn blade]

i quite like this, i recommended a while back that it be in the pinned message

slightly prefer cambridges stuff tho

[valid narwhal]

Could you elaborate? Is there significant difference in content or some other things between resources offered by oxford and Cambridge?

[wraith mica]

Alright I’m super confused what do I do

On AoPS should I do intermediate algebra or precalc

They are both the same thing

So like which one do I buy

I saw this forum saying that you didn’t need to do intermediate algebra because a lot of that stuff is covered in precalculus

Also precalc focuses on trig and linear algebra

Which one do I get

ANOTHER question

Should I get intro to geometry AoPS to prepare for AMC 8,10,12 and do the Olympiad geometry online course for aime/usajmo stuff

[normal crystal]

I don't think they're the same in their books
you can compare the ToC and see any overlap

[wraith mica]

Ok. I mean I’d say that I’m relatively good at a lot of the stuff covered in intermediate algebra but I haven’t mastered it yet

I checked both tocs and excerpts

[vital bane]

You're...Heisenberg

[sterile horizon]

No, my name is kanen

[vital bane]

No

you're supposed to say

"You're goddamn right"

https://tenor.com/view/heisenberg-walter-white-breaking-bad-gif-12563603

[crystal estuary]

https://tenor.com/view/heisenberg-walter-white-breaking-bad-gif-12563603

[valid narwhal]

Sry for the ping, but it would seem that a lot of lecture notes from Cambridge are down and cant be accessed. Would you happen to know the reason why?

[vital bane]

Nice pfp

[crystal estuary]

Thanks

[hybrid sigil]

I think the links haven’t been updated. For example I looked at Tom Körner notes on “Algebra and Geometry II” which currently gives “file not found”. I googled professor’s name, found his home page that has working links to his lecture notes and realised that you need to replace “twk” with “twk10” in the original links to make them work. Here is a working link for “Algebra and Geometry II”: https://www.dpmms.cam.ac.uk/~twk10/Alg.pdf

The others seem to be trickier to fix, but you can investigate, likely it’s just because some overhaul of their websites. It’s probably possible to use Web Archive to find those lecture notes (if they were archived), or maybe write to the professor’s email and ask them nicely 🙂 Or just use Oxford’s notes which work fine, they are definitely good, Oxford is in top-10 unis of the world in math 🙂

[north summit]

Can someone recomend me a cheap combinatorics and graph theory book. Or at least <50 usd

[valid narwhal]

Tysm

[fallow cypress]

(deleted some spam ping messages)

[sleek python]

To find all the pdfs in this website you can search for: site:http://www.dpmms.cam.ac.uk/~twk10 filetype:pdf
or site:http://www.dpmms.cam.ac.uk/ filetype:pdf

I think this should work on most search engines, but in case, it works fine on duckduckgo

Tho if the pdfs have been taken out of the website then it shouldn't work (and in that case go to web archive)

[vestal osprey]

I would appreciate it if anyone has a article or book that is a complete amd rigorous account of discrete differential geometry and discrete exterior calculus?

[hybrid sigil]

A follow-up: this looks like a quite comprehensive set of Cambridge math lecture notes by Dexter Chua! https://dec41.user.srcf.net/notes/ (referred to on the Cambridge site itself - as yet another source of lecture notes)

[hollow peak]

I think Keenan Crane has a good reference

https://www.cs.cmu.edu/~kmcrane/Projects/DDG/paper.pdf

Idk if I would call it complete and rigorous though

[vestal osprey]

Last I checked it wasn't either

But I still have it

In my reference forlder

I mainly would be happy if.anyone has good articles or complete references in the subject

[valid narwhal]

I’ll keep that in mind, thanks. I think I’d start with the oxford ones since especially it starts in a more friendly way

Looking at oxford’s introduction to complex numbers, it defines one as a+bi rather than (what i think is the correct definition) an ordered pair (a,b) in R^2. Assuming that you’ve read a significant portion of their lecture notes id like to ask if they become more rigorous later

[gray gazelle]

what book changed the way you think the most? for me it is probably one of dan fridmans little books

probably wouldnt of gotten into emacs if it werent for those books

[tiny gulch]

Make it stick: the science of successful learning

Probably

[gray gazelle]

ah awesome ill look into it

[valid narwhal]

In linear algebra 1 it also doesnt justify why dimension of a vector space is unique

[gray gazelle]

thanks so much for the recommendation

[slow roost]

there's no one correct definition of a complex number, various definitions are equivalent. You can also define it as an element of R[x]/<x^2+1> or other ways. a + bi is a friendly way to go

that is to say, a + bi is not necessarily unrigorous

you can say i formally satisfies i^2 + 1 = 0 and take R[i]