book-recommendations

[gray gazelle]

please suggest a book for that

actually i was reading folland for that but it gives me trouble

[foggy quest]

I'm pretty sure you'll have trouble if you don't understand Fourier analysis on Euclidean space and the Torus well

[gray gazelle]

okay so chapter 2 and 3 i have to read from your book

[patent canopy]

hello

[solar cedar]

Hi, I started going through Gallian's contemporary abstract algebra. I'm doing the introduction exercise and I find there to be many question, a lot of which don't have a lot of depth. Are there any abstract algebra textbooks whose exercises are fewer in number and are more in-depth (problems sheet style) questions?

[molten gulch]

<@&268886789983436800> sharing pirated materials

[compact copper]

@patent canopy please do not share these in this server, it's against discord ToS

What you do in DMs is none of our business, of course

idk if this book is copyright free but I'm deleting this as well to be safe

if it is not copyrighted feel free to relink

[mellow sage]

Hello !

Can you guys suggest me a book on Conics

[patent canopy]

sorry

[patent canopy]

oh i see, sorry

[compact copper]

it's okay, don't sweat it too much ♥️

[patent canopy]

ok to reiterate, I was suggesting Spivak and Apostol (1&2) for calculus

[keen grail]

Does anyone have any book recommendations on odds and outcomes of very basic casino games like blackjack, Texas hold em and craps? I’m trying to learn as much as I can.

[north summit]

can someone recommend me a read about "Natural density" https://en.wikipedia.org/wiki/Natural_density

[normal crystal]

I googled for similar books
and google suggested every other book by the same author

[humble spire]

look at the references wikipedia links at the bottom?

[jade terrace]

does anyone have suggestions for starting linear algebra? thank you :)

[floral lantern]

Do you need linear algebra for math majors or for engineers?

[jade terrace]

just math

[floral lantern]

There’s a pinned post with advice.

[upper estuary]

It's true, but depending on the prison they may or may not be allowed pencils as they are sharp objects

Perhaps chalk is ok (?)

[urban shore]

Hi does anyone have any books for how maths and art/music are connected?

[gray gazelle]

did you watch 3b1b video on music and measure theory

[urban shore]

Just watched it and discovered his channel thank you!

[pearl goblet]

Any good book on real analysis?

[rough umbra]

#book-recommendations message

[pearl goblet]

Thx

[heady ember]

Inserts John Wick pencil gif

[fresh skiff]

Stephen Abbott

[trail hemlock]

tao

[gray gazelle]

apostel is very nice

\

[elder pier]

bro is casinomaxxing

best use for maths

[sly jolt]

Just learn basic probability

If you apply it right the probability you covered in high school is more than enough to calculate odds in any card game

Khan academy almost certainly had everything you need

[solar cedar]

I'm bumping this question again since it seems to have been missed: #book-recommendations message

[sterile pelican]

Any bad books in algebraic number theory? :^)

[full cairn]

You don't have to do every exercise, you can just skip the boring ones. But if you want a different book, Fraleigh is pretty nice. Its exercises are divided into computations, concepts and theory, so you can do a few of each type

[gray gazelle]

neukirch is very bad for begginers

[sterile pelican]

Thank you...? I didn't expect a proper answer :^)

[gray gazelle]

niether i expect this question

[sterile pelican]

I thought to spice up the section by asking something like that

[slim dock]

Guys could anyone reccomend me a (free online) book for :
Olimpiad geometry
Linear algebra
Calculus
And could there possibly be good books on these which provide complete solutions? The last time I tried reading a math book, I couldn't study any thing cause they don't provide solutions bru

[full cairn]

I bought a book holder seems to work pretty nicely, it's struggling a bit with Lee maybe, but who wouldn't

[gray gazelle]

where did u buy the lee book

[gray gazelle]

i want to buy it, in affordable price to learn cohomology

[full cairn]

bought it online, through a university bookstore

[gray gazelle]

how much u paid

[full cairn]

you can also buy it on springer for 50 EUR with free shipping: https://link.springer.com/book/10.1007/978-1-4419-9982-5

[gray gazelle]

thats too much money

[full cairn]

I paid 56 EUR or something

[gray gazelle]

oh no man

let me get contigency

[molten gulch]

The further you go, the less solutions you will find, it is prudent that you get good at checking your own work. Most university level books will not have solutions. You will not find one book for all the subjects, you will have to search around for them. Do you want proof based or more computational texts?

[foggy quest]

How can I see what link you deleted? If it was https://mtaylor.web.unc.edu/notes/lie-groups-and-representation-theory/, this is a link to the author's website where he has a link to the notes. It's not copyrighted, as you can see by reading the notes.

[compact copper]

I don't remember what the link was and I'm not going to go searching for it

you're welcome to repost any non copyrighted material

such as that

[patent canopy]

hello @full cairn on a similar note, is there a comprehensive book where i can learn Riemannian geometry, Differential geometry, Convex Optimisation, mainly for applications like Optimisation on manifolds from a Machine Learning perspective?

[stable flicker]

There was a suggestion about optimisation books in #optimization
I don't know all of them but I recognise the authors at least

[full cairn]

I don't know much about convex optimization, sorry. Lee also has a book on Riemannian manifolds btw

[gray gazelle]

lee should not be considered for riemmanian geometry(absolute begginer)

do carmo is right

[patent canopy]

and also it feels like Wikipedia

[patent canopy]

btw not a beginner, but a grad student with good knowledge of Riemannian geometry, just want to refresh and re-explore

[patent canopy]

thank you

[patent canopy]

thank you

[full cairn]

The gateway drug

[fresh skiff]

I will use it as my first course in general top

[tribal crow]

[keen grail]

I did stats and business stats in college but I’m looking for something a little more specific but if that’s it I’m good then

[normal crystal]

there are a few books by mathematicians on gambling games
just search on amazon

[keen grail]

💕

[remote sparrow]

sure

[tough crypt]

Hi, I'm approximately a 10th-grade student and I want to learn university-level math in topics like geometry, probability, and calculus in a way that is understandable.
Can you recommend a book?

[cerulean steppe]

have you learned high school calculus?

like AP calculus BC in the U.S.

[tough crypt]

Not yet i have just finished 9th grade

But i want to read some myself

[tough crypt]

Here we start calculus at 11th grade

[lunar wave]

its not a book but I think khan academy has calculus ab and bc if you need example problems

[molten gulch]

Stewart's Calculus

[tough crypt]

Do you have sth for probabilities or geometry too?

[cunning elk]

a full treatment of undergrad probability usually requires at least some background in calculus

[lunar wave]

yeah

true

[molten gulch]

blitzstein and hwang stat110

[cunning elk]

discrete distributions are just combinatorics for the most part

for continuous distributions you need calculus

[molten gulch]

geometry? do you want differential? algebraic? computational? etc...

[tough crypt]

Thanks a lot

[cunning elk]

if you want to learn more Euclidean geometry try EGMO by evan chen?

[tough crypt]

Well i don't know what they mean 💀

[cunning elk]

high school geometry is very very basic Euclidean

[tough crypt]

So should i go for calculus first?

[lunar wave]

what have you taken already alg 1?

and geometry ? or no

[tough crypt]

Well I don't know how the education system works there

Here we just have math

Till 9th

[tough crypt]

Not yet

[cunning elk]

do any of the following ring a bell:

linear equations of one variable

graphing linear functions of one variable

exponential and quadratic functions of one variable

solving quadratic equations in one variable

systems of linear equations in two variables

might want to have a look on khan academy or smth to see what topics you still need to learn

I’d recommend looking at their “algebra 2” topics?

[lunar wave]

as I remember it khan academy had pretty good information for algebra 1 and 2 it might be good to start there

[tough crypt]

Ok

We have technically finished all the topics i liked* in school

Is that good?

[rose flume]

You decide

Right?

[tough crypt]

Decide what?

[rose flume]

If you think its good

Or maybe good but not enough considering you want to learn some higher level stuff

[tough crypt]

Well i was just thinking is that good for 9th grade or i could do more?

[lunar wave]

only you know if you can do more really

if you're understanding everything and you think you can understand more theres no harm in trying

[rose flume]

Does this idea elicit desire within you?

If so, pursue it

If not, why do you want to be convinced that you should do more

Because it felt easy?

[tough crypt]

Well those are what we learnt in school

[rose flume]

I meant rather the idea of learning more math

[tough crypt]

I want to show off my math in the next school year and i have 3 months of summer break

So i want to use it the best way possible

I know that sounds dumb don't mind it

[rose flume]

I dont think that sounds dumb

I think the best way possible is to relax

Rather if I ask you to study some math for the next year right now are you happy doing it?

[tough crypt]

Yes?
I have to do so anyway

[rose flume]

I just wouldnt force myself for an idealised goal on what is considered to be a “break” period

Easy then

Well I think it is a good idea

[tough crypt]

Like i have started physics

[rose flume]

Oops kind of off topic, oops got to sleep 1:30am, oops exam in 30something hours, so see you around, and enjoy learning throughout the summer

[tough crypt]

3am here what a coincidence

See you later

Thanks for all the help everyone 🙏🏻🙏🏻🙏🏻

[willow geyser]

,iam not studying

[hasty eagle]

No selfroles matching not studying.
See ,selfroles --list for the list of valid selfroles.

Jun 18, 2025, 12:34 AM

[willow geyser]

,iam not studying!

[hasty eagle]

No selfroles matching not studying!.
See ,selfroles --list for the list of valid selfroles.

Jun 18, 2025, 12:34 AM

[willow geyser]

,iamnot studying!

[hasty eagle]

Removed the studying! role from you.

[daring wolf]

#book-recommendations

[pure geyser]

You want one?

[full cairn]

I think they're just politely pointing out that this is #book-recommendations , not #post-random-images-and-spam-bot-commands

[pure geyser]

Oh ok

[slim dock]

I know most books don't have solutions, but someone told me that there are a few. I was hoping that maybe some people here would know. Also, I wasn't looking for 1 book, that was a grammar mistake. I'm looking for 3 books, 1 for each of the topics I mentioned

[normal crystal]

there are definitely problem books with solutions for calculus
for geometry but maybe not Olympiad focused
maybe less for LA

[slim dock]

That's bad. And I'm looking for a free book too, so ig this won't work out

Thanks for the explanation tho

[normal crystal]

if you want free free
you can just collect all the OER calc and LA books
do only the problems you want with full solutions
idk about olympiad geometry, ask in comp math channel

[willow geyser]

oh i didnt mean to mb

[old terrace]

Active Calculus can check solutions, iirc. I think Paul’s online math notes does too. They don’t fully explain the solution to every problem though.

For single variable calc, Khan Academy (which isn’t a book) explains solutions well with the hint feature

[slim dock]

I have used the khan academy course before, but their course for multivar is incomplete, thats why i am looking for a math book

[normal crystal]

https://ocw.mit.edu/courses/res-18-016-multivariable-calculus-recitation-notes-fall-2024/
and the OCW course it links

[opaque wasp]

anyone like the aops books?

[fresh skiff]

there was a girl i guess she used aops books

sorry i forgot her name

[heady ember]

free online book
If you search at the correct places, nearly all books can be found in an electronic form at no monetary cost.

[solemn depot]

yes.

[hollow swan]

Someone suggested me a category theory book, I forgot the name

It's like a general book, does anyone know?

[tiny gulch]

I don’t think I was that person but I did put some recommendations here a few days ago - #book-recommendations message

[hollow swan]

Leinster category theory?

Alright gotcha

[novel lake]

Anyone got any good pre graduate calculus book reccomendations?

[old terrace]

For calc 1 and calc 2 (other times called BC calc or single variable calc), Khan Academy is great. As are Active Calculus and Paul’s Online Math Notes

I’ve heard good things about Stewart’s Calculus, but never read it

[fast latch]

,iamnot studying!

[hasty eagle]

Removed the studying! role from you.

[pliant wadi]

What's the dorina mitrea book with an allegedly good account of Fourier transforms

[gray gazelle]

Grafakos' Classical and Modern Fourier Analysis

[torn crypt]

There’s Grafakos as mentioned, but David Cruz-Uribe + Duoandikotxea have a Fourier Analysis book that is also great for exposition without so much getting lost in precise constants

[gray gazelle]

What's your background?

Do you know measure theory? Topology?

[torn crypt]

(And Grafakos’ proofs in those weeds do have a handful of errors, as with any book, but bad enough that a Ph.D. Student I knew who was a few years in was hung up occasionally on those constants)

The book you are referring to is likely the partial differential equation book though by Dorina Mitrea

https://link.springer.com/book/10.1007/978-3-030-03296-8

I do not know much extensive information on this text, so I’d kinda recommend Duoandikotxea, but idk your background, goals, or an in depth description of exactly what is covered best in each text

[vital bane]

I think James often recommends this book

[torn crypt]

Yes

It’s a different kind of book to the ones I suggested, I think, but maybe it’s preferable

[vital bane]

What are the prereqs except measure theory? FA?

[torn crypt]

I’d assume some FA is good

[grave scroll]

I need a Bio/Med mathey stats book
this is the syllabus but I would love to go beyond

if possible suggest me two books
1 covering the syllabus
2 covering something Bio related in depth via maths

[pliant wadi]

Yep

[pliant wadi]

Absolutely that'd be considerably comfortable

Than without

[ancient creek]

Oh dam, I am going to start bio med next semester, there will definitely be good resources.

[grave scroll]

pls send me a list or anything of all books u r using I'm quite excited

[gray gazelle]

Grafakos should be good 🙂

Depends on what your goal is actually

[pliant wadi]

I am trying to understand microlocal analysis actually

So in order to get to it

I was working out morse lemma and stuff

And I know zilch about Fourier transforms except for a bit from QM

[torn crypt]

Well, I’d recommend Duoandikotxea, I also am a bit biased from conversations with people involved in the book, and Peter Hintz’s notes on microlocal analysis and a bit of Hörmander cross referencing can help with the microlocal stuff

[low lion]

Hi, is there someone that can recommend books for Math/Economics? (so that combination)

[pine tundra]

Like arithmetic and geometric progression?

[deep moat]

I suggest reading an algebra book or going online and read a topic about Arithmetic, Geometric, and Harmonic Sequences!

If you want, you can practice some easy to hard problems on AoPs :)

[earnest notch]

Someone could recommend me a book for Linear Algebra

[tender river]

you need to provide some info about your background. plus what kind of a book are you looking for? one about matrix computations? or one that is theoretical and focuses on proofs, usually targeted for pure math majors?

[earnest notch]

Matrix computations, undergraduate

[tender river]

popular books for that are

https://hefferon.net/linearalgebra/

https://njohnston.ca/publications/introduction-to-linear-and-matrix-algebra/

For video supplements, there is:

https://youtube.com/playlist?list=PLOAf1ViVP13jmawPabxnAa00YFIetVqbd&si=Lt5dysELPCXtA3H3 [Johnston's YT playlist]

https://youtube.com/playlist?list=PLwF3A0R8OzMoMlE1-SaEh8h9VqUlO-r52&si=xBDCdPyMzwcnhhaO [Hefferon's YT playlist]

[earnest notch]

Ty!

[fallen frost]

what about like quantum computing and AI for people in high school

[timber mesa]

I don't know any good introductory texts for the first, presumably you'd want to read some of e.g. Beck's Quantum Mechanics first and for that at the very least you'd want to know linear algebra and differential equations, and that's ignoring previous knowledge of classical physics

For machine learning (assuming you mean that by AI) you could check out https://mml-book.com which includes the necessary mathematical preliminaries, ideally you'd want to learn linear algebra, vector calculus and probability first and then use the first part of the book as review though. It's definitely not written for people in HS but a very dedicated 12th grader or something might be able to work through the whole book in about a year

if you only care about the practicalities of ML for data analysis a good start is UHelsinski's online course https://courses.mooc.fi/org/uh-cs/courses/data-analysis-with-python-2024-2025

they also have a discord server for their courses https://study.cs.helsinki.fi/discord

[floral lantern]

For quantum computing, Mike and Ike is the standard (I think the linear algebra is self contained).

It is an actual textbook that involves mathematics.

[normal crystal]

Marlins, a High Schooler, using the exception to answer

[wraith cave]

first you’d need a base in calculus and linear algebra for anything quantum mechanics-based

[fallen frost]

thank you everyone :D i'll definitely get started on this

[normal crystal]

there are some pop sci QC books
they are not pop sci book fans here🤡

[orchid otter]

Anyone got a good recommendation on a Multivariable calculus book?

[snow sage]

Any recomendations for physics involving calculus for a beginner ? I know next to nothing about physics but would to like tostart self learning it

[floral lantern]

Active

[normal crystal]

my scarlet letter, I know

[floral lantern]

I like colley

[round egret]

what aops book should i start with if i just finished ap calculus bc curriculum

[remote sparrow]

does aops have a multivariable calculus book?

[normal crystal]

no

Evan Chen does

[dapper root]

Craig active holyyy

[normal crystal]

all my sins on display

[novel hound]

What is a good abstract algebra book for slightly harder problems than D&F? I did D&F a while back and want to review. I don't wanna go to Lang level. How are Knapp problems?

[old terrace]

I’ve never read Knapp, so I don’t have an opinion there.

Rotman’s Advanced Modern Algebra is great and harder than D&F in my opinion (probably easier than lang, although I’ve never read it. Rotman is easier than grad Hungerford in my opinion)

[tender river]

Herstein, jacobson, allan clark, dixon-problems in group theory maybe

[sterile pelican]

Aluffi?

[remote sparrow]

they asked for harder problems

[grave scroll]

Have a look

[hard mango]

Beginner or intermediate?

[fresh skiff]

Statistics

[grave scroll]

can be anything else I wan bio :]

[fresh skiff]

Idk about bio related such book. We used a book written by our professor (ofc a local book, you wouldn't find pfd) and covered some of the initial topics, the remaining topics will be covered soon (after summer break)

[stable flicker]

Sorry, but this isn't very mathy. The closest suggestions I have are

https://faculty.cengage.com/works/9780534399429
https://www.openintro.org/book/stat/

If you want something mathematical, you can do
https://link.springer.com/book/10.1007/978-3-319-28341-8

[tender river]

What does bio med mathey book mean anyway

probably does not include measure theoretic probability like panaretos

[stable flicker]

I would hope not.
Abstract stats is a thing but I don't see any relevance to biostats

[foggy quest]

"A First Course in Probability" By Sheldon Ross covers the math behind the syllabus. Beyond the syllabus is probability theory and statistics theory used in Biostatistics and statistics literature, covered in https://sites.math.duke.edu/~rtd/PTE/pte.html, "Asymptotic Statistics" by van der Vaart, https://link.springer.com/book/10.1007/978-0-387-74978-5, "Weak Convergence and Empirical Processes" by van der Vaart

[stable flicker]

First Course is fine.
The other books you're describing are off the charts and not what I think a beginning undergraduate in biostatistics should read

To be fair you did describe them as "beyond the syllabus" which is quite an understatement IMO

[foggy quest]

I know, they are the probability and statistics material he should read next. Of course, knowledge of real analysis is needed for Durrett and beyond

[stable flicker]

They are really good books though. I think practitioners (engineering, not-pure-or-applied-math) in grad school should read them

IDK if a stat program goes into those books within undergrad

[crude belfry]

Does anyone have any Linear Algebra book recommendations? I’m a physics student interested in pure math, I’m looking for something proof based, but I admit I have little experience in proof writing.

[vital bane]

Linear Algebra by FIS i.e Friedberg, Insel and Spence

[orchid pollen]

Linear Algebra Done Wrong by Sergei Treil is good

https://www.math.brown.edu/streil/papers/LADW/LADW-2014-09.pdf

It’s open source

[quartz stratus]

Could someone recommend me some good books on set theory?
I've already read Elements of Set Theory by Enderton, but I wasn't a fan of how the book is structured.

[native cradle]

chat, any suggestions for books on math and climate change

[remote knoll]

Naive Set Theory by Halmos is a book I own that I've thumbed through, seems good. And the cover is the best meme

[native cradle]

I've head a lot about naive set theory by halmos

[remote knoll]

And best part is it's short, so if it sucks you're done with it quickly

[native cradle]

wait, you have that many springer books?

wow

[vital bane]

Nice

[native cradle]

my copy is grey lol

[vital bane]

Abbott detected, opinion accepted

[native cradle]

and not by springer

[remote knoll]

I collect math textbooks

[native cradle]

I wish I had the will power to organise my books like this

[remote knoll]

Hahahah they are absolutely not organized

I have pictures of my collection

In the thread

#1379640090149650493 message

[native cradle]

Based

made better by the cat

[vital bane]

Sour Drop's got competition

[native cradle]

I have a huge collection of ||JEE books||

😭

like atleast 50

[heady ember]

Christ

All I see is

https://tenor.com/view/dh9511dh-empty-wallet-hurt-look-away-gif-13355852

[remote knoll]

I buy only used

Most books I get are between $5 and $15

[quartz stratus]

Thanks mate I'll read it and let u know how it goes.

[remote knoll]

For instance

[quartz stratus]

AYOOO, you own that many books? Bro is goated 🔥.

[native cradle]

most of my books are 5 -10USD new ( subtle flex)

[vital bane]

too relatable

[spring wing]

9.99 in my country I get for 90 cents to 2-3USd

[viral bone]

Hello All. Im going to start self-studying linear algebra and I enjoy proofs and abstract thinking if that makes sense.

With that being said, would you guys recommend “Linear Algebra.. Done Right” by Axler? I heard its more abstract/formal.

Otherwise I was going to go with Intro to Linear Algebra by Strang.

For the record I already have some minor knowledge in “matrix math” if you wanna call it that. Also once I transfer out of CC ill be required to take an LA class of some sort regardless. Its just im trying to learn it faster because Im starting to need it for ML.

Any suggestions would be appreciated, thanks.

[tribal crow]

I don't think LADR is a bad choice for your circumstances

I've never properly read it though (I used FIS instead), so hopefully somebody else will give you some better insight

if you're interested, Dami wrote a very short review of the book in [this post](#book-recommendations message)

[viral bone]

Thanks

[viral bone]

Ill read this now

[normal crystal]

learn faster for ML and taking it again later
sounds more like use Strang

[trail kelp]

hello. can anyone suggest me a good book for trig and algebra?? ( I am a high school student )

[viral bone]

Yeah, I might just pirate both and then see who I enjoy reading more.

I do hear strang tends to be more conversational? But its less abstract and so.. If I’m going to learn anyway.. might as well.

Plus even if axler doesn’t necessarily focus on computation I should still be able to apply the concepts, no? Idk. Ill probably get axler because its not over $200 dollars

[normal crystal]

ixnay on the pie rah say here

[solar cedar]

One exercise set I'm doing in Gallian's contemporary abstract algebra has a total of 91 questions. I can't do every question, nor can I judge what questions would look good from a glance. Would you recommend taking a random sample of 1-91 and doing the associated questions?

[tender yoke]

why can't you judge which questions look good from a glance

surely some of them look more interesting or accessible to you

[remote sparrow]

did you know this is available as a dover?

[grim ore]

Only true if the edges are also red

[outer terrace]

Try solving blackbook pinkbook and yellowbook 🐸

[elder stratus]

just look up the name of the book online and you can probably find a pdf, no need to pay any money

[cerulean steppe]

I used https://mtaylor.web.unc.edu/notes/linear-algebra-notes/ and liked it. The latest edition of Axler's book is pretty similar. This book also looks good: https://www.math.brown.edu/streil/papers/LADW/LADW.html/.

[outer helm]

how it’s 9,99$ 😭

[grim ore]

its even half price o.O

[outer helm]

every time I buy books it’s at least 40-50€...

[viral bone]

Thanks

[grim ore]

same but in usd so its higher

atleast 60-80

[outer helm]

yep 🥲

[remote knoll]

I wasn't aware, but I'm not surprised

[remote knoll]

Gotta be patient and go in person to your used bookstores

[heady ember]

Nice. I don't really see any second hand math books here, unfortauntely.

[heady ember]

Two tomes of analysis: measure theory, to be specific.

[vital bane]

Huh

Is bro printing out and binding both volumes of Bogachev?

[heady ember]

No

[ancient creek]

Oh I thought you were trying to visualise lebesque integral

[heady ember]

The one below was sewn some time back: Bass's measure theory book. The one above is Dietmar A. Salamon's measure theory book, which I have just finished sewing.

I also have fully binded Folland's measure theory book a couple months ago

[ancient creek]

🔥

[heady ember]

What a bookbinding flex.

[vital bane]

110,000 subscriber special

[heady ember]

10 000 special

He sewed the signatures and spine together exactly like this. That is, it isn't a cop-out of gluing the regularly-binded signatures with a hardcover that is separately sewn for the 10000, if you get what I mean.

[old elk]

:o

[vital bane]

Have you finished learning real analysis? Usually that's a prerequisite for proof based ODE books

No, learn real analysis and then come back

[old elk]

And linear algebra

Sotomayor

[fresh skiff]

Wow

[fresh skiff]

I usually have seen measure theory as a prerequisite for proof based differential equations

[daring wolf]

diff eq for enginners is not proof based

like they just learn the results and how to solve it

over why is this true

[livid ginkgo]

hi

[vital bane]

keyword "proof based" 🗿

[torn crypt]

If you want a higher level one, there’s also (the start of) Jech

The later chapters are maybe not some grand expository work, but like the first half or so?

Not my area per se but you’ll certainly figure things out enough to find what works for you

[torn crypt]

I don’t think I’ve seen those two before but nifty

[torn crypt]

There’s also Teschl that comes to mind, idk about Strogatz

[ancient creek]

Have you heard of the most powerful theorem? It's called the fundamental theorem of engineering, very very powerful.

[craggy path]

@teal cedar

[teal cedar]

hi

[craggy path]

1. Problems In Calculus Of One Variable by IA Maron

2. Principles of Mathematical Analysis by Walter Rudin

3. Introduction to Number Theory by David M. Burton

4. 104 Number Theory Problems by Dorin Andrica, Titu Andreescu, and Zuming Feng

5. Problem Solving Strategies by Arthur Engel

6. Mathematical Olympiad Treasures by Titu Andreescu and Bogdan Enescu

7. Mathematical Circles: (Russian Experience) by D. Fomin, I. Itenberg, and S. Genkin

8. Geometry Revisited by HSM Coxeter

9. Inequalities: A Mathematical Olympiad
   Approach by Bulajich Manfrino, Radmila, Gómez Ortega, José Antonio, Valdez Delgado, Rogelio

i had this list saved

[teal cedar]

oo

[teal cedar]

all the titless don't really sound welcoming

[craggy path]

idk i just ssaved the list

[teal cedar]

that's alright, ill take a look on each of them

[craggy path]

yea

[native cradle]

Any book suggestions on books examining the intersection of climate chnage and maths

[empty flume]

Hi, can someone suggest me some books on number theory

[bleak slate]

i cant :/

anyways i wanna read lolita so bad but like my teachers are gonna think im psychopathic athgargharghagrhgrahrgg 😭 cuz who the hell reads that sht in like middle school 💀 🙏

[vital bane]

💀

I wanted to read moby dick, but it is no longer on my shelf

[bleak slate]

sad

[cinder magnet]

Rudin sounds like a bad idea

[brisk rapids]

How much do you know?

[gray gazelle]

hello can anyone recommend me some most basic pre university math books? thanks 🙏🏻

[pliant tartan]

what maths books should i read for my personal statement ? i know thats a very broad question but im not sure where to even start in the first place

[gray gazelle]

I'm a math exploring beginner

[brisk rapids]

in what sense? as in how do you want this help for your personal statement?

[pliant tartan]

i want to broaden my understanding of maths beyond the high school level i was taught as

[brisk rapids]

I guess How to Solve It by Polya might be nice.

[pliant tartan]

i want to look more into number theories too

[pliant tartan]

ty!

[brisk rapids]

This (https://infinitedescent.xyz/) is new but I've heard good things about it. I've not gone through it myself.

[brisk rapids]

You can try looking through the first few chapters of Ireland Rosen but it might be too much.

[pliant tartan]

alright ill check it out, tysm!

[median fossil]

Not a big loss

[vital bane]

really?

it's not that good? it seems to be a classic

[vital bane]

Change the "Mathematics" to "Madness" in the title and it will be changed

[median fossil]

Classic does not imply good

[median fossil]

Personal opinion ofc

[vital bane]

True

[median fossil]

I've found most of its "philosophical" blabber not to be that philosophical or deep

[vital bane]

Philosophical blubber

[median fossil]

It somehow reads better if you don't take it seriously but (can't find the right nuance of second degré) ironically(?)

As in, laugh at it

[vital bane]

This somehow feels like a very French way to look at it

[median fossil]

[sterile pelican]

Do you know how to write proofs?

If you know proofs you probably can do Silverman's A Friendly Introduction to Number Theory, I quite like that book

[gray gazelle]

what is proof bro? 😁

[sly jolt]

People don't realise that there's literal twitter accounts with more philosophical thought than classic books these days

There was no easy way to share a single thought back then so you'd get a general overarching message and write an entire book. That doesn't hold up to today's standards of throwing out like 30 takes in an hour. But such takes don't generally go as applied as in classics

[sterile pelican]

I like reading philosophical classics they are nice to read

Whether thay hold up to now I am not sure but I think they carry some nice findings. Like reading Euclid's Elements sure they don't hold up to modern geometry but they have something nice to offer

[median fossil]

There were plenty great philosophical works published at the time. Which were more profound than the overwhelming majority of modern "takes". Also deep things are often more subtle than something that can be expressed in a Twitter post-sized take

[sterile pelican]

Honestly, I think reading Twitter philosophical quotes kind of robs the important subtleties too (well reading Twitter at all isn't exactly an enlightening read overall either)

[median fossil]

Also when I say philosophical works I'm thinking of literature with a message here

[fiery steppe]

What are your opinions on Abstract Algebra by W. Judson? (https://judsonbooks.org/aata/)
It was a nice alternative to some of the more traditional AA books that I found on a few MSE posts.

[molten gulch]

Some like it

[stable flicker]

afaik it's free which is a huge plus

afaiik it's open source too but I don't remember if that is true

oh ya it's open source

huge plus plus

[fiery steppe]

Yes it is free and open-source

[empty flume]

Not much I think so

[heady ember]

Indeed: https://github.com/twjudson/aata

Plus, SageMath exercises

https://tenor.com/view/spy-family-anya-anime-clap-wow-gif-142883711582845267

[stable flicker]

Crazy how this list is so small
https://link.springer.com/search?new-search=true&query=&content-type=textbook&openAccess=true&dateFrom=&dateTo=&facet-discipline="Mathematics"&sortBy=oldestFirst
Anyone recognise the Differential Geometry books?

If anyone has opinions on

DG
https://link.springer.com/book/10.1007/978-3-031-39838-4
https://link.springer.com/book/10.1007/978-3-031-51462-3

AG
https://link.springer.com/book/10.1007/978-3-031-88819-9

please say them! Always worth talking about freely available knowledge!

[humble spire]

wikisource has moby dick for free

[vital bane]

Yea I can find most books for free

but physical copies are just nicer

[humble spire]

yeah ❤️

do you have a library containing it near you?

[vital bane]

I think I might

[heady ember]

Amen.

[fresh skiff]

Metric AG

[vital bane]

I will help you grass 👍

(no I wont)

(because I don't know anything )

[vital bane]

First time I'm hearing about this too

[heady ember]

Its ok: monke together stronk.

[vital bane]

Where is this from?

[heady ember]

Source: https://open.umn.edu/opentextbooks/textbooks/how-we-got-from-there-to-here-a-story-of-real-analysis

[vital bane]

dayum

peak

[molten gulch]

what book is this from?

[molten gulch]

Oh I just saw this

[vital bane]

Hey I know this book!

This should be pinned tbh -> https://open.umn.edu/opentextbooks/

[heady ember]

No no what should be pinned is my website with all the open source links I found while procrastinating

[vital bane]

grass:

Oh nice Axler's books are here as well

Based Axler

[heady ember]

I haven't engaged with foundations in a long time, unfortunately.

[agile flume]

Those look nice

[stable flicker]

Sounds cool tbh.
But yeah list too small plz contribute!

[heady ember]

Nearly all books are free anyway

[heady ember]

@vital bane

Since I don't wanna dox myself, I just slapped my website's .md file into a PDF converter

[sturdy shore]

love this

[stable flicker]

MathCord listed

[stable flicker]

Why not just post the .md here? Like as a text blob in discord? I don't think anyone will find it a spammy post

[heady ember]

Ok

[stable flicker]

Discord allows .md formatting too, won't require too much issues formatting it

[heady ember]

[stable flicker]

lgtm!

Let me see

Wait no

That's the HTML formatting

[heady ember]

In my website's file it's an .md file. But I guess it uses HTML too.

[stable flicker]

You can send it in 2 posts

(Collated by @heady ember )
Some legally free resources:

• Organisation
  • AMS Open Math Notes
  • MIT OpenCourseWare
  • ISI Open Course Ware
  • American Institute of Mathematics Open Textbook Initative
  • Springer Open Access
  • UPenn Online Books Page
  • Open Textbook Library
  • Tau Beta Pi (UCB Exam and Syllabus Database)
  • π-Base
  • Math Counterexamples
  • EqWorld
  • Merlot (Multimedia Education Resource for Learning and Online Teaching)
  • Lambda Calculus Visualizations
  • Free Mathematics Web Journals
• Student
  • Dexter Chua
  • Andrew Lin
  • Eigentaylor (LA)
  • Ang Yan Sheng (ANT, Comm Alg, MT, SCV)
  • Clement Yung (Jech solutions)
  • Student Set Theory and Combinatorics Seminar

(Collated by @heady ember )

• Professors see #book-recommendations message
• Qualifying Exams
  • Make Me A Qual
  • Stanford Past and Practice Qualifying Exams
  • UW-Madison Qualifying Exams
  • West Virginia University Qualifying Exams
  • UCLA Quals
• Social
  • Mathematics Stack Exchange
  • MathOverflow
  • Mathcord (Discord)
• YouTube
  • Richard E Borcherds (Intro NT, Complex Analysis, Algebra, Categories, Lie Groups, Comm Alg, AG, AT, Rep Theory, Hom Alg, Modular Forms)
  • Sheldon Axler (LADR Lectures)
  • Timothy Gowers
  • Antonio Montalban (Set Theory and Logic)
  • Mathcord Lectures (Logic)
  • James ash (FA, MT)

[molten gulch]

You forgot the UCLA quals page too https://ww3.math.ucla.edu/past-qualifying-exams/

[stable flicker]

must be something in my copy paste

original message: I've nothing against UCLA

(Also Collated by @heady ember )

• Professors
  • Terence Tao
  • Sheldon Axler (LADR, MT)
  • Sergei Treil (LADW)
  • Cayley Graph Plotting
  • William F. Trench (Intro RA)
  • Michael Taylor (Intro RA, intro CA, MVA, DG, PDEs, etc)
  • Keith Conrad (LA, Algebra, ENT, ANT, Analysis, Topology)
  • Thomas W. Judson (Algebra, ODEs)
  • Ivan Khatchatourian (Topology)
  • Gerald B. Folland (MVA)
  • Ravi Vakil's The Rising Sea (AG)
  • Jean-Pierre Demailly (Complex Analytic and Differential Geometry, Potential theory, Hodge theory, AG)
  • J.S. Milne (Algebra, Lie Algebra, AG, ANT, Etale Cohomology, Hodge Cycles, Motives, Shimura Varieties, Elliptic Curves)
  • Charles Weibel (Motivic Cohomology, K-Theory)
  • F. W. Lawvere
  • T. S. Blyth (Module Theory: An approach to linear algebra)
  • Dietmar A. Salamon (Measure theory, FA, DT, DG)

[molten gulch]

lol that's fine

Mods should pin this

[fresh skiff]

Wdym? I didn't even read anything else except metric AG

I am using FIS as my main Linear algebra text. I am thinking to use Axler for problems (so skipping theorems and theory can i directly do exercise problems as well?)

[stable flicker]

Become a professor and publish open access

[fresh skiff]

Oh right ! ! !
If ever i become able it will keep things for free ..

[vital bane]

FIS has plenty of problems

[fresh skiff]

True, i should say some others. Usually half of the exercise problems in FIS are computational. Moreover i have done most of the problems (upto chapter 3). So looking for some new

[native cradle]

I'd also add project gutenberg , but yea, really nice list!

[native cradle]

@fallow cypress can this be done?

( sorry for the ping, didn't want to ping the entire mod team)

[molten gulch]

also hey wai hpe you're well today

[molten gulch]

Thanks eric

[fallow cypress]

just ping mods

[stable flicker]

I'll add cr to gwass then

[native cradle]

Hi!, How are you doing?

[native cradle]

Sorry

[stable flicker]

Hmm idk how search-friendly gutenberg is, but yes a lot of old books are worth a lot

[molten gulch]

good

[native cradle]

[vital bane]

gutenberg mentioned

printing press inventor/distributor

[remote sparrow]

i doubt anyone will care

[golden escarp]

Hi! Can someone please help me choose a book about the rise of modern logic? Right now I am aware of the following options: W. Kneale and M. Kneale, "The Development of Logic"; I. Grattan-Guinness, "The Search for Mathematical Roots"; and P. Mancosu, R. Zach, and C. Badesa, "The Development of Mathematical Logic". I think Kneale’s treatment is rather early (it stops at Frege), which does not match my interests; Mancosu et al. seem a bit brief, since they largely ignore developments before 1900. Ideally, I would like something similar to Corry’s "Modern Algebra and the Rise of Mathematical Structures", covering roughly the 19th century up to about 1930 (Goedel, Tarski results). For now, I am considering reading Grattan-Guinness’s monograph, but I haven’t heard many opinions about it, so I’m not sure. Does anyone have more suitable suggestions?

[foggy gorge]

Would someone suggest me any abstract algebra book for an early undergrad student?

[cerulean steppe]

chapters 6 and 7 and appendix A of https://mtaylor.web.unc.edu/notes/linear-algebra-notes/

chapters 1-3 cover linear algebra, a necessary prerequisite for 6-7

[foggy gorge]

Oh

Thx

[full cairn]

IMO those notes might not be the best choice for a first exposure to abstract algebra, I would recommend a book like Fraleigh, Gallian, or Aluffi's Notes from the Underground

[old elk]

Dummint?

[full cairn]

Sure I guess, I don't have strong opinions on that book

[fierce needle]

There’s a book by Marco Hien, which claims to be especially designed for self-study.

[fierce needle]

I’ve heard from other people that it’s an excellent book.

[foggy gorge]

I'll download that one

[normal crystal]

you saw that YouTube
didn't ya

[fierce needle]

Perhaps. If you mean the honest torus, then yes. They also have a discord server.

[normal crystal]

yea, that was the one I saw
I didn't know he has a discord server
there was another book on Amazon I saw after watching that video that seems similar in viewpoint and also German origin
https://www.amazon.com/dp/3319951769/

[torn crypt]

Ooh metric

[torn crypt]

Skill issue

[gray gazelle]

yoi

[lime frost]

Fellas , I kinda need a rigorous numerical analysis course, Ive done the standard engineering numerical analysis courses, but its more a collection of techniques but they dont teach you how to prove a particular method converges or ways to create my own.

Does anyone have any recs for books or lecture series
ok, didnt send only half the message this time

[kind stream]

does anyone have an algebra textbook for 7th or 8th grade?

[molten gulch]

OpenStax https://openstax.org/details/books/elementary-algebra-2e

[tribal crow]

@kind stream welcome to the mathcord!

[kind stream]

thanks

[raven hedge]

I recommend Chris McMullens book on practice problems but to actually learn it from a textbook, the big fat Algebra 1 textbook is your go to.

[austere thistle]

Can anyone recommend a good book for learning quaternions? I’ll need to study this topic for robotics and graphics in the future. I want to study it now using a formal mathematical approach in my free time.

[heavy vault]

ts prolly belongs here

[shrewd stream]

hello

[heavy vault]

ig more generally do u guys think like reading a book from a high level view on all the topics before you dive into the weeds is a good idea

[shrewd stream]

what math books you reccomend for a high schooler for competitive math

[heavy vault]

art of problem solving

[shrewd stream]

both vols as in?

[heavy vault]

yea js start with the general volumes

also make an account on their website they have a very robust community for competitive math stuff

[shrewd stream]

ahh

[raven hedge]

Hi

[timid lion]

can you clarify what you mean?

[hollow narwhal]

Is this good?

[sterile pelican]

Is it for your course?

[idle fulcrum]

yo guys hellom nice to meet yall

do you guys hav a book recommendation for the basic math

[gray gazelle]

Read the three little pigs

its good

[stable flicker]

Use any calculus textbook

[upper estuary]

For basic math Khan academy is great

Not a textbook but it saved my life :)

[idle mortar]

Man I am planning to do something noice

[heavy vault]

No ig I js mean in like a really big picture sense do you think it makes sense to read a book that gives you a birds eye view of undergrad topics like ra and topology to understand the big picture before diving deeply into each subject

And does a good book like that exist or should I js start with classic recommendations for each subject (like axler rudin munkres dummit and Foote etc)

[gray gazelle]

Does anybody have a book recommendation for linear algebra that also talks about applications to quantum mechanics?

[vital bane]

The only source I know that does this is chapter 1 of Shankar's QM book

[gray gazelle]

oh 😭

[gray gazelle]

so.. would you recommend doing a book dedicated to linear algebra and then after that, a book for quantum mechanics?

[dire cobalt]

3b1b

its a yt channel , not a book

but he is goated, bro made me understand linear alg in grade 9

also used for calculus

i would kill to have him as my teacher

[vital bane]

Perhaps, but I don't know much, maybe there is a LA book that's focused on applications to QM

[gray gazelle]

Truetrue

Already watched most of his videos though

[sturdy shore]

what does 3b1b have to do with applications of linear algebra to quantum mechanics

[sturdy shore]

disclaimer: not a physicist

But I believe applications of LA to QM shouldn't be so different from functional analysis, which is kind of Axler's thing

so, I'd say LADR, but I doubt you'd go wrong with any other LA book really

you'll just have to switch some notation around once you pass to QM, like vectors become kets adjoint * becomes a dagger inner product is now antilinear in the first component etc etc

[gray gazelle]

Got it, thanks!

[sturdy shore]

actually, there are also giant books that focus on "math for physicists" type of deal and they'll have LA sections, I'll try to find one but looking at them you'll probably realize what I said is true

[jade cape]

Does somebody has a book

For calculus?

[molten gulch]

thomas

[jade cape]

Is there any book to get from dummy to overpowered in calculus?

[jade cape]

Thomas?

[molten gulch]

yes

https://www.amazon.com/Thomas-Calculus-Early-Transcendentals-14th/dp/0134439023

[jade cape]

Ohh

Snap

How long does it take to master?

[molten gulch]

I went through it over the course of a year in two uni courses, if self studying, just take your time and do a good amount of the exercises

[sturdy shore]

Found the book I was thinking of: Mathematical Physics by Hassani

It's like a ~1200 page giant, its first 200 pages is about linear algebra

[gray gazelle]

got it, will look for it! Thankss

[sturdy shore]

it's absolutely not a math book as in, it just states stuff and doesn't prove it (by and large) through a cursory glance maybe it proves like half the theorems?

may have some extra material in there like on algebras over fields as well

I'd recommend going through something like LADR instead, but can use this book to compare notation and transition to physics

[stable flicker]

This looks like a cool book!

[sturdy shore]

yeah the content is really exciting, should be a good reference for especially mathphys type people coming from math who need to get accustomed to physics notation

[raven hedge]

I really recommend Chris McMullens books on Alg1, geometry 1, calc 1, physics, etc.

[true sail]

Hello, I'm rather new to proofs, even though I had a course on Hilbert-style axiomatic systems. I would like to improve my proving skills, is the Jay Cummings' "Proof" book good to learn how to write proofs?

[raven hedge]

I think so yes

Though, if you’re looking for more logic proofs, I recommend ForAllx by Calgary.

A great book on proofs and learning logic

[true sail]

Are "logic proofs" like pure "Prove that p -> p from the axioms"?

[dire cobalt]

he taught linear alg

[north summit]

Which complex analysis book should one choose if primarily interested in learning analytic number theory?

[upper lynx]

someone has a good book (or more books) that cover these topics:

affine geometry
euclidean spaces and isometries
hermitian spaces
normal operators
bilinear and quadratics forms
projective spaces

[remote sparrow]

stein and shakarchi or freitag and busam

[simple root]

hey guys do you know any good calc books in german?

[fading mango]

i just recently finished high school (a level maths, further maths). so any good introduction to university maths? im not sure where to start.

[simple root]

https://github.com/ossu/math

[fading mango]

seems great

thanks

[timid lion]

particularly i think you should start with discrete math

here’s what we use: https://www.math.uci.edu/~ndonalds/math13/notes.pdf

[fading mango]

why do you say this?

[tribal crow]

@gray gazelle @timid lion welcome to the mathcord!

[fading mango]

hmm. this isnt the kind of discrete math im familiar with.

i take the discrete math module in fm and we learn stuff like graph theory and linear programming so i didnt expect abstract maths which seems like a good introduction

[timid lion]

yes basically

the one i linked is not discrete math per se but it covers a lot of what our discrete course covers

the rest is graphs and stuff as you mentioned

• combinatorics

[tender river]

the usual starting points for pure math are analysis, and linear algebra, some start with algebra, or number theory or combinatorics. Theyre all fine. You could try to read the start of terrance taos analysis book to get a feel for pure math maybe

[graceful hamlet]

cool list of physics books https://www.youtube.com/watch?v=Cw97Tj5zxvA

[gray gazelle]

Thanks

[normal crystal]

weren't you just asking for similar books

[vital bane]

That sounds very wrong

[normal crystal]

it does
but it is an accurate description of a wide swath of literature

[vital bane]

I don't know much but I think misery literature might be more accurate

[normal crystal]

but the derogatory term is more fitting

[raw otter]

This a really good thanks a lot

[normal crystal]

Chipper
that and the reading books on a phone screen
your life is an ergonomic hate crime

[vital bane]

Hard times create strong men

🗿

[normal crystal]

Chipper will be the half blind hunchback hero
the world needs

[tawny crater]

ive started reading hatcher and it seems there are some pre-reqs im missing. for example, he mentions genuses of manifolds without pausing to explain, and I haven't seen that in my manifold class. Is there a good source to catch up with?

[daring wolf]

I don't think this is a necessary prerequisite. You can just proceed without having extra materials imo.

While smooth manifolds(~de Rham Cohomology) gives some bunch of intuitions, i dont think they are necessary.

[tawny crater]

ok, ill try my best then

googling the concepts that are unknown will suffice?

[gray gazelle]

Sup? I'm trying to (self)learn algebra from scratch to master inequalities, piecewise functions and everything else in between. Can you guys point me towards some quality resources? I'm modality agnostic so it can be a mixture of text-based, video based, or interactive, as long as there're practice questions.

[molten gulch]

https://assets.openstax.org/oscms-prodcms/media/documents/Algebra-and-Trigonometry-2e-WEB.pdf

[gray gazelle]

OpenStax! What a great start. Thanks a lot, friend.

[hard valley]

why is foundations first illegal?

[marble fern]

Heyting algebra books? Pls ping

[mossy flume]

Heyting?

[remote knoll]

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

[mossy flume]

Oooo

[remote knoll]

@marble fern I don't know much of anything about this subject; however, there's a math.se post on the topic.

[marble fern]

Thankuuuu ❤️

[old elk]

https://friedl.app.uni-regensburg.de/papers/1t-total-public-october-7-2024.pdf

[graceful moon]

Yeah definitely, Hatcher is a just a bit weird, the prerequisites are pretty minimal though, you definitely don’t need to know about manifolds

[old elk]

Hi guys for those who know about group theory rings modulos and galois, I would like to know which book I should follow, which is the best content to follow and well structured, I have an idea of the topics but I would just like to study it in an orderly way and with a sequence that helps me to understand this area, I have 8 months to understand and strive in the group theory and if I reach a part of the ring theory.

If you believe that the contents as they are in these books are not adequate what would be the order to follow under their knowledge I would appreciate it very much.

[graceful moon]

If you have plenty of time, and want a nice order to learn the subjects in Dummit and Foote is definitely the way to go

It’s long and wordy, definitely too much so at times, but it’s incredibly thorough and complete

[timber mesa]

can't go wrong with Dummit & Foote it's a classic and rightly so

other books might offer different points of view and presentation, might be worth reading another in parallel

[old elk]

Definitely Dummint I find it a bit weird how he presents the topics to me, let's give it to him, thank you very much, hope to see you in the group and channel rings :3

[graceful moon]

Yeah if you find anything weird about it you’re more than welcome to ask in #groups-rings-fields and you should try some other books to see how you feel about them. Artin is another pretty comprehensive option but there’s a big chunk of linear algebra in the beginning

[gray gazelle]

Hey, thanks again for sharing the link. Here's where I'm at so far:

[timber falcon]

@timber falcon

[peak dew]

Does anyone have "elements set theory solutions" pdf
I'm reading elements set theory and I need to check my solutions

[old terrace]

Khan Academy is pretty solid. It doesn’t cover absolutely everything, but it has videos and lots of great practice problems.

I’ve heard good things about Professor Lenard’s YouTube videos, but never watched any of the algebra ones

[rain hound]

openstax is so good

[gray gazelle]

I second this.

[gray gazelle]

I checked out Khan Academy earlier, and I'm familiar with their work. Good stuff- soothing to watch too, haha. Yeah, I'll incorporate their videos into my learning plan. Thanks for the recommendations!

[heady ember]

Just check your own work, or ask in #proofs-and-logic when unsure.

They're probably referring to an unofficial solutions manual.

[peak dew]

Some times I feel people overreact on trivial matters
like I do sometimes
But it's okay 👍

[peak dew]

np 👍

[torn crypt]

If you want an analytic POV, Pedersen covers the normal operators and such, but perhaps not what you seek

[remote knoll]

Please do not request pirated material on the discord. It is against TOS to share pirated material.

[torn crypt]

So, this is a bit of a troll recommendation, but Sheaves, Games, and Model Completions by Ghilardi, Zawadowski

[remote knoll]

Doubly so because it's a solutions manual. Academic dishonesty is not permissible on this server.

[torn crypt]

The recs here are good too, and wrt the modal logic book there’s also First Order Modal Logic, a springer book

It’s similarly about modal logic

But the first order part means you get quantifiers and such, completeness things, etc

That said, idk what’s in that book they mentioned as well, so perhaps it’s all redundant but it’s very recent

[marble fern]

Sharp hath noticed me :o

[torn crypt]

It’s a troll rec since it’s only indirectly about them, or categorical things, but it does stuff wrt intuitionistic logic and that relates to Heyting etc

But it’s good stuff for those purposes

[marble fern]

I'll probably be too dumb to get it tbh

[torn crypt]

How else does one learn but reading books they don’t already understand

[marble fern]

Is it normal to be relatively good at logic but also kinda oof at basic integration?

[marble fern]

By reading books they sorta understand

[torn crypt]

I’d like to think that described me for a good while, but perhaps arrogant to think I’m good at integration or logic now even

[torn crypt]

true, but you will know when you try and read

[marble fern]

The humility :o

Yeah yeah I'll get to the books

Between you and me... I'm not even a maths major (yet)

I'm an engineering major

Should I switch?

I was thinking of doing maths cs next year

I mean do you think it is kewl

[torn crypt]

Don’t make a decision on a whim

Speak to advisors on potential issues with graduation, consider career prospects, etc

[marble fern]

Prolly coz you ain't 31337

[marble fern]

I did look it up I'd continue second year (so I won't lose any time)

And I can always go do quantum computing after it

Coz I'm sure I'd be better than most at it

I'd have the competitive edge

Edgin

Idk

[torn crypt]

Well, as long as you consider it carefully

Anyhow, logic stuff in first year is rare

(Or ever, tbh)

[marble fern]

Not a maths major

Die

[torn crypt]

Anyhow, you say relatively good, do you know about types in model theory

[marble fern]

I know about type theory and there's types in model theory being I think 1st order statements

[torn crypt]

I’ll take that as a no

[marble fern]

😔

[torn crypt]

Well do feel free to use the handful of logic channels tho

[marble fern]

Is it different to type theory?

I kinda only know one type theory theorem

[torn crypt]

Yes

[marble fern]

The proofs as terms

Book recommendations?

[torn crypt]

That’s an important thing

[torn crypt]

Well, lectures on the curry Howard isomorphism and a course in model theory are good books

But don’t neglect, like, algebra and analysis and all

[marble fern]

True

Thanks sharp, huge fan

[torn crypt]

You’ll get there, and you can go as hard as you want, but don’t rush by neglecting things

[marble fern]

New lectures when?

[torn crypt]

One day perchance

[marble fern]

Perchance..

[drowsy pine]

3 body problem

Oh is this for textbooks

Sci-fi is goated if u like fantasy

Funnily enough I used to be scared of scifi as a kid but now I love it

3 body problem

tho some of the physics was p hard for me to wrap my head around

Probably

Wdym like epic

ohhh yea

there’s probably a lot

[valid ridge]

Hey everyone! So I’m starting my undergrad in Data Science this year, but I’ve been really wanting to get serious about math through self study. I know high school-level math pretty well, but I’d love to build it up properly over the next 4 years so I can eventually do a master’s in something that blends computer science and mathematics.

If you guys have any solid book recs, lecture series, or online courses that helped you learn math from scratch to an advanced level, please drop them here! Would mean a lot. 🙏✨

[timid lion]

I'm going into my third year as a Math & CS major. It depends what kind of math you want to do, I'm assuming as Data Science you are interested in statistics. You will also probably take calculus, linear algebra, and discrete math as courses. If you have taken Calculus 2 already, a place I started "advanced level" math is Spivak's Calculus, which goes over Calculus 1 and 2 at a deeper level and introduces some abstract math concepts like sets and induction. Discrete math will likely cover these. If you want a plan to follow, you can reference the requirements for your school's math major, and learn from those course notes or the textbooks they use.

[regal arch]

Hi I need a book for IOQM/RMO exam. I am currently in class 9. Suggest me some solid book(/s).(IOQM/RMO exam is a preliminary exam in India for qualifying in IMO)

[regal arch]

If possible text me privately too

[old elk]

Maybe because I am used to the analysis books, and they are always linear in the contents, that is to say they explain almost the same thing but the books maybe with other notations or more examples but as for the theorems I have always seen that they are linear, but as for the group theory many authors explain the contents differently for example in the case of dummint, that's why my brain says what the hell?

[viral bone]

Are there any books for calculus like LADR where he assumes its your second pass through but also “starts from the beginning like you know nothing” and goes over like the rules for why and how things work? I find it interesting as Im piecing it together page by page.

So I wonder if theres a calc version..? Idk if youd call LADR proof based? Im only a couple pages in, and Im by no means a math major. But like its very like abstract I guess? Like setting the rules for why things work instead of telling you a formula and plugging stuff in

[graceful moon]

Are you just confused because different authors present results in different orders? This is also true of analysis

[loud cradle]

if your first pass through calculus was not proof-based then spivak

[graceful moon]

That’s nothing to worry about really, it’s just a stylistic choice for the most part* (excluding stuff like chapter 0 which does category theory super early etc)

[viral bone]

Thanks Ill look into it

[native cradle]

chat, any diff geo book reccs

Kristopher Tapp's books is good?

what does he assume.I know

[old elk]

I was reviewing it and the truth is good, but I do not like the way he writes in terms of definitions, it's just a matter of taste, otherwise I give it 9.5/10, I wanted to buy it but I can also recommend this book that is also new.

[native cradle]

Which book

[old elk]

You can also use the book of Don Carmo, excellent book, although I live more in love with the book of Kristopher.

[old elk]

If you are right some books explain first limits continuous functions derivatives and integrals and then topology on the line, I think that's the variation that makes, I'm talking about real analysis of calculus avazando because also real analysis that is the theory of measurement of course, that if varies topics

Only that the correspondence of theorems for example explaining that the kernel of a homomorphism is a subgroup is the subject of subgroups leaves me as good if you are right is a subgroup, but should be in the topic of Isomorphism and homomorphism because there should be I think, are things like that.

[fresh skiff]

Hi sheep raider

[old elk]

Hi Afzal

[foggy quest]

I like the several variable book here: https://mtaylor.web.unc.edu/notes/math-521-522-basic-undergraduate-analysis-advanced-calculus/ supplemented with the section on multilinear algebra (aka tensors) here: https://mtaylor.web.unc.edu/notes/linear-algebra-notes/ or Lee's smooth manifold book

[native cradle]

thanks

[misty dew]

Hi
I am going to enroll an electrical engineering degree, and I wanted to know how should I prepare for university
I thought about studying linear algebra to get a head start
What do you think?

[remote sparrow]

https://www.webtoons.com/en/fantasy/the-spark-in-your-eyes/list?title_no=3210

[old elk]

Yes!

My brother is in electrical engineering, He studied a lot of linear algebra and applied calculus, and then electromagnetism.

[last cipher]

hs teacher gave me this book from the school math department office archives 👀

The table of contents are very unique and i cant believe this was even in a hs

[molten gulch]

this looks like a discrete maths book with some basic linear algebra alongside

[last cipher]

yeah

ive never seen a book be combined in this manner tbh

[full cairn]

Plus probability for some reason 🤔 interesting table of contents

[molten gulch]

Most discrete maths book have discrete probability within them

[last cipher]

Heres the last chapters contents

[molten gulch]

I will admit, groups rings and fields in the back is quite rare at this level

but outside of that most of the material seems bog standard

[last cipher]

oh yeah fs

[molten gulch]

Also you doxxed your HS with that barcode at the top

I don't know if that was intentional

[last cipher]

oh oops

thanks lol

[molten gulch]

np lol, if you do want to repost that cover, just blur out that barcode using snipping tool or something

[last cipher]

ofc

this was a GREAT find

its published originally from the 1980s

i think i might take a look into it especially since it touches on some 1st year uni material lol

[heavy thorn]

Name?

[last cipher]

Vectors, Matrices, and Algebraic Structures by H.A Elliot, K. D. Fryer, J. C Gardner and Norman J Hill

Its Canadian 🇨🇦🇨🇦🇨🇦🇨🇦

[rich sun]

what every hs graduate should know

[heady ember]

Wait I just realised: the whole 'professors' section is missing. When you are free, do you mind editing it in?

[brittle quarry]

Just found something crazy

Signed copy of a Graduate Text in Galoi Theory by Edward’s

[remote sparrow]

who signed it

[slim helm]

galois

[brittle quarry]

Harold M. Edwards

[heavy thorn]

I've seen a Cornell professor advising students to do galois theory before algebra

Specifically this book by HM Edwards.

[brittle quarry]

Yeah

He’s right —

Galois Theory contextualizes the concepts of modern algebra

And provides the necessary motivation that most modern algebra texts lack

[mortal ore]

intuitionistic galois theory i presume

[analog wadi]

can someone recommend me a book about inequation?

[cunning elk]

if you're looking at olympiad level inequalities specifically try this to start? https://artofproblemsolving.com/articles/files/MildorfInequalities.pdf

[last cipher]

I found a website on weebly that basically explained the whole thing. Worth a read because it reveals a hidden part of Canadian Mathematics education at the secondary school level https://historyofnewmath.weebly.com/

The reason why I'm so surprised is because math education in Canada is kind of watered down imo

[cunning elk]

you dont need linalg for those basic kirchhoff rules systems

and the kinds of examples they give you are usually the "nice" ones anyway

op nvm then

^ has never taken beyond intro physics

[normal crystal]

Strang?
maybe you can watch his video lectures
in epub

Chipper, that's probably what you were asking for though
the textbook

the videos are more aligned with the 5th edition fyi

you read epub textbooks on a phone
and you're complaining about the OCW vidéo quality

the New Vision of LA videos of his are better video quality since they're newer

https://ocw.mit.edu/courses/res-18-010-a-2020-vision-of-linear-algebra-spring-2020/

[paper star]

Is plane trigonometry by loney good enough?

like I'm in my 11th grade and tryna learn trigonometry in rigorously

[paper star]

I just know that I'm not bad with maths and physics stuff, i just need a proper book to guide me

[naive lava]

you probably don't need a separete book for trig

it's not a huge topic

[spare osprey]

Hello guys

Is anyone studying real analysis recently ?

[naive lava]

I did

like a few months ago

[molten gulch]

New math had a few good bits but it was far and away quite a failure as far as I am aware due to it being too abstract and people not getting it well

But there are ofc residual bits of it now embedded in the curriculum

[stable flicker]

Sorry, not without breaking non-nitro limits

[stable flicker]

I repurposed a near message to contain it

[analog wadi]

thx

[heady ember]

Its okie

[heady ember]

Nice, thanks

[native cradle]

chat, any good open source hard RA books

[gray gazelle]

hi what is some good courses for high school maths

[edgy hare]

On the same theme as youssef's question I guess:
What are some good books or free resources for filling in gaps in math education?

[molten gulch]

What level did you stop/have gaps at

[molten gulch]

You need to be more specific

[cloud crane]

Hi is there any book recommendation for studying abstract algebra up to algebraic geometry?

[molten gulch]

Have you studied any Alg before?

[cloud crane]

Olympiad oriented algebra

[edgy hare]

I dropped out around covid, would have been precalculus. But I know I've got random gaps throughout my education, lots of health problems. Ideally I'd take more college classes but I don't have money for that

[molten gulch]

That's not abstract algebra

[cloud crane]

Exception for inequality

[cloud crane]

Oh yeah

[stable flicker]

The only one I know is by Jiří Lebl, and it's probably the only one.
But if you want just a free book there's more, like Axler's MIRA

[cloud crane]

Sorry i thought alg in general

[molten gulch]

I see, https://openstax.org/subjects/math

this has some texts

[cloud crane]

I was studying about group (basics stuff)

[molten gulch]

there's also this https://www.stitz-zeager.com/Precalculus4.pdf

[edgy hare]

Thanks!

[native cradle]

I'm just starting RA 😭

[molten gulch]

I see, https://judsonbooks.org/aata-files/aata-20240706.pdf is a common recommendation to get started

[native cradle]

I'm currently doing seqeunces will do toplogy of R this week

[molten gulch]

There's also Artin, which I absolutely adore

[native cradle]

judson is pretty good, yea

[molten gulch]

Beyond that you have the so-called grad level textbooks like Jacobson, Lang, Hungerford, Rotman, etc...

[native cradle]

Though if you're willing to spend a bit ( say 10 usd) , artin is good too

[molten gulch]

you should at-least casually know a good amount of the material if doing an AG book like hartshorne

[native cradle]

atleast Artin is 10 USD where I an

[cloud crane]

Okay thx. Where can i find a problem in abstract algebra other than a book?

[molten gulch]

Well you should see where you can apply symmetry and rewrite different problems into those about groups

[stable flicker]

I think MIRA is for RA starters, isn't it?

[cloud crane]

Okay okay

[molten gulch]

MIRA is for measure theory

[native cradle]

no 😭

[cloud crane]

Alright thanks

[native cradle]

it's a graduate level book

[molten gulch]

Also for alg geo, if you want a taste; there's the book "Ideals, varieties, and algorithms" by Cox Little and O'Shea; it assumes you know only some linear algebra and a tiny bit of abs alg, and I do mean small, at-least to start the book; take a look

I'm reading it rn, it's quite fun

[cloud crane]

Do analytic number theory need a knowledge in complex analysis?

[molten gulch]

though some examples do assume you know calculus

[molten gulch]

absolutely

[cloud crane]

Ohh i ever heard that book. I think i will start it after learning some stuff in AA and linear algebra

[molten gulch]

Stein and Shakarchi, Freitag and Busam, and Ahlfors are common choices for proof based CA

I know churchill is also common but that's a very computational text a-la what may be used in a "complex variables" course

[cloud crane]

Alr, i think i will grind first in calc, AA, linear algebra, Real and complex analysis then move to advance part.

Thx for the recommendation.

[stable flicker]

wtf the only other freely available book in undergraduate RA is the one by Trench

[foggy quest]

There's also the books here by M. Taylor: https://mtaylor.web.unc.edu/notes/math-521-522-basic-undergraduate-analysis-advanced-calculus/

[stable flicker]

Looks standard

[native cradle]

Thanks

One last question( I've asked multiple times but about to buy so want to be sure)

troppe is a good book for DG right

[gray gazelle]

Anyone can recommend Books about Set Theory?

So far I had one from Bourbaki

[native cradle]

does tapp's books have exercises at the end of each chapter

[molten gulch]

halmos naive set theory

[hallow iron]

is this only for math books recommendation?

[tender river]

channel description says

Use this channel to ask for book recommendations. Tends to be mostly math but feel free to ask about other literature (YMMV). Check out https://mathematics.gg/books too!

[remote sparrow]

no

[hallow iron]

ohh okk

[foggy marsh]

Any good books for number theory and euclidean geometry. I want to prepare for IOQM

[native cradle]

.

[cloud crane]

I use
Number Theory : Modern Olympiad Number Theory
Geo : Euclidean Geometry Mathematical Olympiad by Evan Chen and A Beautiful Journey Through Olympiad Geometry.

[gray gazelle]

Thx

I just got a pdf of this via university access 80€ for a book is expensive ngl

[gray jungle]

that's cheap for academia standards, welcome aboard

[molten gulch]

it saddens us a bit how expensive textbooks and monographs can be

[last cipher]

80 dollars for 300 sheets of paper and a cardboard cover

[timid lion]

can always look for good course notes from lecturers instead!

[humble spire]

Its for free on internet archive 💀

[gray gazelle]

I got it for free through university access

[weak drum]

you can google any book title with the word "pdf" alongside it... except for some psychology books for some reason

[trail hemlock]

tcc is gonna get u bruh

[last cipher]

Any good introductory complex variables textbooks

[onyx ridge]

i know 😔

[last cipher]

Was thinking

but im open to anything

[cerulean steppe]

https://mtaylor.web.unc.edu/notes/complex-analysis-course/

[gloomy spire]

What are the best biographies on Emmy Noether (if any, but it feels like a crime for there not to be)?

[cerulean steppe]

AI suggested me "Proving It Her Way: Emmy Noether, a Life in Mathematics" by David E. Rowe and Mechthild Koreuber, "Emmy Noether – Mathematician Extraordinaire" by David E. Rowe, and "Emmy Noether: 1882–1935" by Auguste Dick.

[old terrace]

I used this one in undergrad and liked it

No idea if it’s better than the one you proposed though

[trail hemlock]

nice cover

[native cradle]

Asking for someone I know, any good open source CA books?

[old elk]

Bravo

[native cradle]

Found the pin

[heady ember]

You sniped me

Looks great

[foggy marsh]

Thanks also for combi

[cloud crane]

Idk, i never use a book to learn combi, (i use my native tongue book)

[foggy marsh]

Ok

[normal crystal]

some legit free EE books including the requested here
https://services.publishing.umich.edu/Books/Electrical-Engineering-Textbooks

[normal crystal]

I think the MIT Agarwal book pdf is semifree
like it's on the edX course for free, which is free to join
but that's an atypical book too
maybe look on one of those OER database sites

[half void]

Should i read wiebel homological algebra or bourbaki’s algebre homologique 🫠

[analog wadi]

can someone recommend me a quadratic inequality book? (it doesnt need to be a dedicated one as long as it has a chapter about inequality its fine) it doesnt need to be hard i just want to make sure that i got the basics right

[half void]

I dont think that will help you much. Just watch a youtube video on the subject or something.

https://m.youtube.com/watch?v=_gWjLKsFOPE

[analog wadi]

alr thx

[humble spire]

https://math.libretexts.org/Bookshelves/Algebra/Advanced_Algebra/06%3A_Solving_Equations_and_Inequalities/605%3A_Solving_Quadratic_Inequalities

[analog wadi]

thx

[random estuary]

Could someone recommend me a book for the aime?

[humble spire]

aops volume 1

[pallid crescent]

Great book if u wanna deeply understand Second Year mathematics

[random minnow]

what do you guys recc for a supplement for needhams visual complex analysis for a first time learner?

im thinking conway and gamelin

[cunning elk]

volume 1 is a bit too easy for AIME, if you had to pick an AoPS book I’d say volume 2 (but both of these volumes suffer from being rather outdated)

[molten gulch]

Stein and shakarchi, gamelin, freitag and busam, etc...

[cerulean steppe]

https://mtaylor.web.unc.edu/notes/complex-analysis-course/

[torn crypt]

French? No

Also, Rotman has a homological algebra intro as well, but tbh I’ve never seen the Bourbaki text ever used

[half void]

I’m mathematically bilingual 🙃

[balmy garden]

do you fellas know an intro to RA book that's the following: relatively interesting, primarily not computational, and clear?

[cerulean steppe]

"Introduction to Analysis in one Variable" here: https://mtaylor.web.unc.edu/notes/math-521-522-basic-undergraduate-analysis-advanced-calculus/

[balmy garden]

i'm looking at an MIT OCW course on it

[tender river]

any single book here #book-recommendations message the mit ocw course follows jiri lebls basic analysis

[misty dew]

Do you have any good way to study?
I've already done 3Blue1Brown's course

[bright epoch]

is there a list of texts on the mathematical study of ML someone posted here yet

if not, does anyone have any especially good recs

[molten gulch]

Something like Diesenroth, Faisal, and Ong - Mathematics for Machine Learning?

But this is more prereq maths for ML

[cerulean steppe]

I've been recommended https://www.di.ens.fr/~fbach/ltfp_book.pdf, but I haven't read it

looks interesting

[normal crystal]

you can't post that file here, no piracy
<@&268886789983436800>

[sage python]

Please do not post pirated materials here, it's... Oh deleted

[atomic bay]

ok

[sage python]

But yeah piracy is a TOS violation and our server might get boiled

[tiny gulch]

I think one of his strongest soldiers is just on this server for some reason

[normal crystal]

delete where it was forwarded from too, if you didn't

[atomic bay]

I dont know that this is a pirated copy

[atomic bay]

ok

[remote knoll]

already taken care of

The colors, Duke, the colors!

[atomic bay]

how do you know that this is a pirated book

[remote knoll]

I downloaded it, it's part of the UTM series published by Springer, they don't publish them for free.

[normal crystal]

if it's a copy of a legit publisher's book with no notice it was made OER
assume it's pirated

[atomic bay]

ohh, I downloaded this book from a website

[remote knoll]

To be clear, I have absolutely nothing against piracy personally. It's pretty much the only sane response to book prices being... well, the way they are.

Just it's against Discord TOS to host pirated materials and to discuss methods for piracy on this server.

And it can get the server shut down.

[normal crystal]

I feel like 99.9999% of the people here feel the same
but it is what it is

[vital bane]

It's what it's

[atomic bay]

ok then

I didn't know about this

[remote knoll]

to be fair, it is not mentioned in the #rules because it is a Discord TOS thing.

[atomic bay]

Can you help me to discuss on that book?

[normal crystal]

they do
after they're told they broke the rules
before they get banned
it's a small window

[normal crystal]

you can mention the book author and title to gather people to discuss it
you just can't share the file in the server

[atomic bay]

how to make thread

The book is The four pillars of Geometry

[torn crypt]

M Taylor’s biggest fan

[tiny gulch]

-# to be clear this is not me

[vital bane]

Pseudonium, M Taylor's biggest fan

[tiny gulch]

That’s L

[normal crystal]

idk if L is even a student at UNC
or just appreciates the man and his (free) works

[vital bane]

I thought L was a character from death note

Landscape mode + Zoom in

ez

[normal crystal]

Chipper, write Prof Taylor an email review
be sure to include photos of his books on your phone screen

[vital bane]

"too much scrolling"

Bro is reading a math book like a novel

[daring wolf]

imagine reading math books like a novel

smh lmao

[normal crystal]

he has a laptop too!
he just is a glutton for punishment

[vital bane]

wtf

you have a laptop? and yet you choose to read on your phone...unforgivable...

yes

that's quite literally what it's made for

unlike a desktop PC, which I have

[normal crystal]

Chipper on his phone notes
"TIL a laptop is portable"

I feel like the laptop to couch comfort problem is easier to solve
THAN READING A TEXTBOOK ON A PHONE SCREEN

are you saying it's the mandarin words for red then neck
or "redneck" used as a loanword

[heady ember]

Just... use a table?

[woven hill]

What if he doesn't have one

[heady ember]

That's your problem then

[woven hill]

It's a logical argument

[heady ember]

House
No table
Logical

[woven hill]

I didn't have a table until 3 months ago

The one I got is pretty neat

[heady ember]

[woven hill]

I really like it

It has shelves and everything