book-recommendations

[gray gazelle]

I live really close to one

and it is free

[remote sparrow]

the books you have are pretty standard

i'm just saying, i started buying books and haven't really stopped

[gray gazelle]

good because I asked the prof for standard books

[remote sparrow]

idk about your real analysis book tho

never heard of that guy

[gray gazelle]

I told him that I want to face the same content if I were to take the course in college

[hallow oriole]

its real analysis, it's gonna be fine

[tribal crow]

RA is pretty standardized, so it should all be fine

[remote sparrow]

also differential equations but the curriculum is set in stone too

for better or worse

[hallow oriole]

if they dont like it that's what certain sites are for

for worse

!!

diffeq is the most mindnumbing class oat

[remote sparrow]

giancarlo rota when he sees the average ode book:

[tribal crow]

I heard that ODEs classes are only fun if you make them dynamical systems classes

[gray gazelle]

the version I have

[remote sparrow]

https://tenor.com/view/ltg-low-tier-god-yskysn-ltg-thunder-thunder-gif-23523876

[gray gazelle]

I couldn't find on the internet

of my RA book

[remote sparrow]

yeah i took a two semester ODE class

[crimson leaf]

Did you ever learn proof based linear algebra

[gray gazelle]

literally me

[gray gazelle]

define proof based

[remote sparrow]

first semester was just closed form solutions, basic techniques

[gray gazelle]

but I did study from these two books

[remote sparrow]

second semester we used strogatz

[gray gazelle]

https://www.cs.cornell.edu/courses/cs485/2006sp/LinAlg_Complete.pdf

[remote sparrow]

most other professors did sturm-liouville theory, boundary value problems, and laplace transforms for the second semester

[hallow oriole]

was that the prof who wrote a whole essay on how bad the deq curriculum is

[remote sparrow]

yeah

[gray gazelle]

Linear Algebra with Applications
Steve Leon 10th edition

I guess they are proof based

[remote sparrow]

the guy i had for second semester ODEs is a young guy, he does research in nonlinear differential equations

lot of it is dynamical systems

so thankfully i wasn't subjected to more of the usual ODE crap

[tribal crow]

that's awesome

I might try Arnold for when I learn ODEs (~6 months)

[crimson leaf]

Yeah these both seem like more computational approaches to linear algebra. You should look at reading one of the books on this list #book-recommendations message

[remote sparrow]

hirsch, smale, and devaney is good too

pretty standard book for dynamical systems now

[gray gazelle]

Well , my professor said that he made the course 70% computational
30% proof

[tribal crow]

this is the book my institution uses, and I've heard nothing but bad news about it

[remote sparrow]

also hubbard and west wrote a pretty rigorous book on dynamical systems too

[gray gazelle]

becuz there are some physics majors taking the course

[tribal crow]

I'm not sure if everyone I've asked is just overreacting, but they haven't sold me the book as an appealing one

[crimson leaf]

Yeah I guess ideally you should learn form something that's like 80% proof 20% computational the books on that list are pretty good and I think Sour Drop also has some solid recs

[remote sparrow]

well ryc is a huge fan of hirsch, smale, and devaney

@glad prairie

https://www.amazon.com/Nonlinear-Oscillations-Dynamical-Bifurcations-Mathematical/dp/0387908196

strogatz has this book as a reference in the back

so you have several options

[gray gazelle]

what does R and C mean

[crimson leaf]

R is the real numbers and C is the complex numbers

[gray gazelle]

Works over R and C.

got it

[hallow oriole]

evidence you shouldn't use it

[gray gazelle]

what does anti-determinant mean

[chilly sentinel]

I feel like i'm learning 95% theory in Linear Algebra, should i specifically practice computations or will understanding the theory enough allow me to improvise quickly?

[remote sparrow]

you should know how to do gaussian and gauss-jordan elimination

you should be comfortable with working with 2 x 2 and 3 x 3 matrices

like multiplying them by hand

or finding their determinants by hand

the rest is whatever

[gray gazelle]

finding determinant is annoying beyond 3x3

I was amazed that one can do inverse with gaussian elimination

[chilly sentinel]

which is why we use computers to do it and we just need to know how

[gray gazelle]

unless u r in an exam and u got to do 4x4

[chilly sentinel]

they just wouldn't give a 4x4 because it would take too long and they want to burn your time with more conceptual tasks

[gray gazelle]

I messed it up anyway

[hallow oriole]

i had to find det of a 4x4 on a midterm

[remote sparrow]

i was assigned a 4 x 4 because they wanted to test cofactors

🙄

also usually they give 4 x 4s that have lots of zeros

[tribal crow]

I had to compute a 5x5 generalized modal matrix on my final

[hallow oriole]

only one zero on mine

[tribal crow]

wasn't too pleased about that one

[heady ember]

Hi 🐟-enjoyer

[rigid forge]

whats a quick guide to get started with latex though

[remote sparrow]

https://tobi.oetiker.ch/lshort/lshort.pdf

https://www.overleaf.com/learn/latex/Learn_LaTeX_in_30_minutes

https://www.amazon.com/REAL-ANALYSIS-THEORY-MEASURE-INTEGRATION/dp/9814578541

https://www.amazon.com/Problems-Proofs-Real-Analysis-Integration/dp/9814578509

@sage python possibly the dummit and foote of measure theory?

[glad prairie]

This is insane. Do people just complain its hard?

Its one of my 3 favorite math books

[heady ember]

What are the other two

[viral moth]

as an hs student (with some self-studying of uni maths, mainly with analysis)
i've also had a bit of a look into category theory - so i'm vaguely aware of simple things like short exact sequences and functors
would the joy of abstraction be a good place for me to start learning category theory?

[thorn birch]

hey

[glad prairie]

Strichartz Distribution Theory and Fourier Analysis, Coudene Ergodic Theory

[thorn birch]

can anyone recomend me geometry book for euclidean geometry?

With lots of exercise... Intermidiate / Beginner level

[graceful moon]

I don’t know catagory theory myself, I’m going to be learning it over summer, but the general advice I’ve seen is not to start with catagory theory. It’s much better if you have some background in algebra and topology first apparently

That said I do know that books a kinda mix between an expository piece on maths and a textbook, so if you’re reading it for fun it could be good, if you just want a textbook you’d probably be better grabbing one

[viral moth]

i have tried picking up textbooks but i suck at sticking to them

[graceful moon]

There’s definitely people better equipped to answer you, but just warning you about highschool catagory theorists lol

[viral moth]

i mean i know a bit of topology

maybe less algebra

i mean

idk i've never really tested myself so how am i supposed to know how well i know a subject

but i guess i osmosis stuff

[graceful moon]

Yeah I mean I guess the question is just why you’re interested in learning it

[viral moth]

i know a lot of high school category theorists

and like

i guess it's a relatively shallow field to get into

also it might come in handy in undergrad

[graceful moon]

Leinsters book which is often recommended to people says that neither group theory or topology are required prereqs but it’s where most of the examples come from, and 2 of my friends took the course with him

One of them had the background and loved it, one of them didn’t and found it utterly unenjoyable because he didn’t have any context for it

So again, I don’t really know any myself, but I have seen and understand the warnings about maybe just learning some algebra “normally” first

[viral moth]

that is true, i have been neglecting algebra

lemme have a look rq at leinsters book

[graceful moon]

Do note that it’s a textbook and the joy of abstraction is a kinda middle ground

[viral moth]

right

the examples seem fine, like i know what a subgroup is and i know what a hausdorff space is

[gray gazelle]

The whole point of category theory is that it reframes the stuff you’re familiar with

You’ll want to have seen homomorphisms, canonical isomorphisms, directs sums/products, quotients, etc. a couple of times before doing category theory

I’d recommend reading an algebra book which touches on categories instead (Aluffi, for example)

[round shore]

When you start, you have to take a lot of time checking that the usual objects you know indeed satisfy the cat theory definitions

[lusty ermine]

any references to get started with commutative diagrams?

[round shore]

Start learning algebra to get used to universal properties (eg: isomorphism theorems for groups, localisation)
There is no really "references for commutative diagrams", it is just a way to write some equality of morphism. Once you have a little idea of how it works for classical examples coming from algebra, I think your goal is to understand the Yoneda lemma. Basically, understanding Yoneda=> understanding universal properties and.... half of category theory

[heady ember]

What did you like about them

[glad prairie]

Theyre clearly written, interesting, well organized, concise

[heady ember]

nice

[glad prairie]

Good examples, good exercises

[rigid forge]

any introductory book to type theory? (something concise and without any major prerequisites)

[heady ember]

Check out Clerk's recs in pinned

Iirc there's a section on type theory?

[rigid forge]

I tried searching, couldn't find it

[heady ember]

Here ya go

[rigid forge]

ah it was in a pdf, thanks!

[tribal crow]

I've heard quite a few complaints that it's dry

some have called it unmotivated

but I'm in no position to assess the validity of these claims

[steel cloud]

Recommend book for module theory

[remote sparrow]

Aluffi's Notes from the Undergrounds covers modules

also check pins

[mental galleon]

Elements - Euclid

https://mathcs.clarku.edu/~djoyce/java/elements/

[gray gazelle]

does anyone know of any lecture notes based on abbott's understanding analysis?

[remote sparrow]

#book-recommendations message

[dapper inlet]

does anyone know of a more rigorous Linear Algebra text ,rn im using David Lays book

[tribal crow]

#book-recommendations message

I personally like FIS (Friedberg, Insel, Spence), but I've seen Axler, Treil, Hoffman/Kunze, and Halmos recommended before

[tribal crow]

there's even more here that you can take a look at

[dapper inlet]

ty

[steel cloud]

Okay

[gray gazelle]

Hi

I want book recommendation for calculus

basic level

[slender cargo]

OpenStax. It's free and well-regarded.

[gray gazelle]

thx

[cursive orbit]

fyi: Springer is 50% off rn with code FLASH50

[trail hemlock]

yeah thats been going on for a while

maybe they forgot to remove code

[remote sparrow]

thanks

[fast coral]

Does anyone here know anything about Peruvian books?

[violet shuttle]

They exist and are probably written in...portugese? Not English

[fast coral]

spanish

i asked because i wanted to know which one is better, racso or lumbreras

[fervent tusk]

Im fairly certain i failed abstract algebra 2, Can anyone give a book that covers the following topics:
rings, ideals, fields, domains, Principal ideal domain, irreducibility of elements, field extensions

if there is an extra chapter on polynomials that would also be appreciated; the textbook required for the class was pretty rough and I need to see more worked examples to be able to do proofs

[narrow relic]

I did not get to those topics in this book but from what I read I recommend it: https://centerofmath.com/textbooks/post/p_2398394

[narrow relic]

It covers all those topics. From the material I read (from Chapters 1, 2, 3) it is extremely clear and has examples. Also, it's only $15.

[lusty ermine]

which book goes in depth into recurrent sequences?

and recurrent relations

finding the limit of those sequences

exercises like that

[fervent tusk]

thanks

[narrow relic]

You're welcome 🙂 Let me know what you think if you end up getting it and studying some from it.

[spiral raft]

suggestions for books on game theory?

[remote sparrow]

#book-recommendations message

[spiral raft]

thanks brother

[gray gazelle]

any good books courses for intro ml?

[fervent marten]

what book should i get that focuses on basics of integration that have a lot of practice problems? for an 8th grader

[orchid dust]

Any books for beginners at mathd

*s

[rich sun]

where do you want to begin

[golden salmon]

a good intro textbook that covers a bit of everything is halliday resnick and walker

[deep moat]

In terms of olympiad textbooks, what're good books that can help me participate in Math Olympiads (first time)? Another is fundamental books before I get lost

At the moment, I am reading an algebra textbook from AoPs.

[orchid dust]

Cool thanks 👍

[orchid dust]

Probably something that covers a bit of everything yk

[pliant wadi]

Where can I find a tad more elaborated version of Spivak's take on Partitions of Unity?

In his book Calculus on Manifolds

Like I still wanna work in R^n but, a bit more detailed.

[stiff blaze]

I think Munkres goes into more detail in his book Analysis on Manifolds

[vocal owl]

I need all your opinions on this list and whether it’s worth studying as a first year engineering student, I’ve sent it in #chill (picture with the list and anime stuff), if it’s not viable or worth it for a first year engineering student recommend me some good books to learn from pls🫱🏽‍🫲🏾

[pliant wadi]

Oh found it, thanks!

[vestal holly]

Are there any site/book recommendations that provide lots of questions to practice high school math?

[karmic tangle]

Has anyone here gone through "Topology Through Inquiry"?

[lusty ermine]

which reference has hard telescoping product exercises

[narrow relic]

Wendell Fleming's Functions of Several Variables has a chapter called on Integration on Manifolds.

[small wind]

can anyone give a good book for starting calculus pleasee

i wanna start learning calculus early cos math is real fun for me

[stiff blaze]

What are your goals exactly? You want a more rigorous treatment of the math that you would see in your engineering degree? Or you want to eventually learn more pure subjects? You should also make a basic timeline of when you plan on finishing each book so you can track your overall progress.

[gray gazelle]

بتعمل ايه هنا يا صاحبي

[gray gazelle]

taking a book recommendation for calc

[gray gazelle]

oh great but why

u done alr with multivariable , no ?

[gray gazelle]

no im great but i want a book to make revision

• I'm having a problem with reading math books

[gray gazelle]

what is ur problem ?

It's simple i can't read books but watching youtube videos is ok

[gray gazelle]

Is it just math or other subjects too?

math and Quantum

if other subjects then that is a not a math problem , that a time span probelm

[gray gazelle]

what topic u studying for math now

shouldn't u be doing linear ?

i have differential

[winged marsh]

Can anyone suggest me a book for problem solving in abstract algebra? I want problems on Groups, Rings, Modules and Fields

[tribal crow]

#book-recommendations message

[pliant wadi]

Oh I'll check it out, thanks!

[winged marsh]

I don't the idea about the questions/examples in these books could you help me with that?

[tribal crow]

oh I misread your initial request

you wanted a book for problem solving in AA

in that case, I'm not the one to ask haha (perhaps wait for somebody else!)

[fierce kiln]

Does anyone know where I could find a PDF copy of the paper "The Representation of Partition Structures" by Kingman? Seems like I don't have access to the relevant journals.

[round shore]

I have acces wait

[fierce kiln]

You're exceptionally kind, thank you.

[spiral raft]

any books to help understand enough calculus to use it in physics?

currently reading feynman's lectures

[plush inlet]

I'm taking a grad level analysis class next semester, but struggled a good bit in undergrad analysis, does anyone have a preferably problem-heavy book that gives a gentle introduction to beginning grad-level real analysis?

[abstract copper]

Axler's is gentle for grad level

[plush inlet]

Thanks, will check it out!

[vocal owl]

My goal is to learn the maths I would i see in the engineering degree and eventually move on to pure subjects as an extension, as for time line I’ve got a timetabling app to track my progress

You got any recommendations? Or would you say the list is valid (i can send you the list on pm so u can look over)

[abstract copper]

Yeah those are not the math you would use in engineering

Engineering math are very computational as far as I know

[vocal owl]

yeah but id like to extend myself down the road you know

Like first get thru the engineering maths then move onto pure as extra/extention

[stiff blaze]

I would go: First Level Calculus by Spivak, Set Theory by Pinter and Linear Algebra by Hoffman. Second Level: Multivariable Calculus (any book) Odes+pdes+ possibly intergral equations if you are interested (I don't have any good book recomendations). Third Level: (computational) Differential Geometry by Pressley, Complex Analysis Ablowitz, Real Analysis by Rudin and Abstact Algebra (at this point I would go with Dummit and Foote and not Fraileigh because you are already exposed to proofs). Graduate Level: Complete Dummit and Foote, General Topology by Willard, Smooth Manifolds by Lee and Measure Theory (I have only read a little bit of Rudins so I cant recommend you a book here). At this point you would basically have completed most Undergraduate Math Courses and the core Graduate ones.

[vocal owl]

Okay thank you🫱🏽‍🫲🏾 I’ll look into all of these

[stiff blaze]

Some notes on the books that you have sent: Basic Geometry isnt necessary. I would rather go with a Set Theory book than an intro to proofs. I don't think the problem solving books will help you too much but they dont hurt to have. Graduate Complex Analysis isn't something necessary to study, if you really like undergraduate complex analysis go ahead, but you can't know this from now. Same with Functional Analysis (if you like the Topology part of Real Analysis or the Spectral Theorem of Linear Algebra then go ahead). Same with Serge langs Algebra. I prefer Willards Topology to Munkres because its just General Topology (No Algebraic), you should get another book on that. Lastly, intro vs non intro books (eg intro Analysis vs Analysis books) dont really have that much of a difference, the later ones usually include more stuff and assume you are familiar with proofs, if you read Spivak and Pinter you will be familiar with proofs at this point.

[vocal owl]

thank you for this

[stiff blaze]

Also don't forget to check out other math subjects such as Numerical Analysis, Probability, Statistics, Number Theory, Combinatorics, Algebraic Geometry, Category Theory/Logic. You might like them.

[vocal owl]

Okay I’ll for sure look into them, thank you so much

[trail hemlock]

what have you learned so far?

[deep moat]

AoPs introduction to/intermediate algebra a good one?

[remote sparrow]

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

[narrow relic]

This Knapp Basic Algebra book looks pretty good

Sour Drop have you worked through any of this?

[remote sparrow]

not yet but i have a copy of it

[narrow relic]

It looks good 🙂
I might switch from Lang to this, I'll let you know my impressions of it if I do.

[trail hemlock]

yes they are great

[golden salmon]

Not exactly a maths request, but is there a recommended text for electrical circuits? Preferrably concise, with questions. I already have Horowitz and Hill if that helps

[dapper root]

guh?

[golden salmon]

aye

[orchid dust]

Do you have a recommendation for a book for school maths?

[plush totem]

i do

concise msths

[supple siren]

any1 help me with a roadmap for class 11 maths

[violet shuttle]

well you can always use google maps instead nowadays

[supple siren]

lol

[orchid dust]

Thank you

[vast jackal]

I have a question 🙋 I'm having a hard time with Khan is Professor leonard good for algebra 1 and 2?

[orchid dust]

Do you know any for ordinary maths

[remote nova]

Yes.

[vast jackal]

I'm trying to for precalculus and then calculus and calculus based physics?

[fervent marten]

what book should i get that focuses on basics of integration that have a lot of practice problems? for an 8th grader

[remote nova]

Sounds good.

[remote nova]

None exists. People don't make books about integration for middle school students. Any book on integral calculus suffices.

[spiral raft]

3b1b essence of calculus is pretty good for basics though

[lusty ermine]

which references introduces reflexive relations in a clear way

[pastel shale]

How good is Statistical Inference by Casella and Berger for introductory statistics? I have prior knowledge of prob and stats but I'm looking for something that I can comb through completely and thoroughly to get a solidify my knowledge, and I dont want to have to go to other resources if this book is enough

https://mybiostats.wordpress.com/wp-content/uploads/2015/03/casella-berger.pdf Heres a link if anybody wants to check it out

[still panther]

any of them? its such a minor topic that i dont even know if there is anything interesting to say

[lusty ermine]

wdym any of them

can you name some

do you mean algebra books in general

[still panther]

maybe i am misunderstanding what you are asking? its just a relation that forall x xRx

there is not much to say about it

[lusty ermine]

maybe, but I would like to get introduced to other relations, like transitive, symmetric, antisymmetric

maybe its basic but where do I read that

[still panther]

I guess any set theory book will deal with them, Halmos or Goldrei are popular picks

[heady ember]

You can probably learn them as you go, instead of reading it from a specialised book.

E.g. Rudin talks about equivalence relations (not saying you should read Rudin, but you get my point)

[still panther]

you should read rudin to appreciate how shit it is or alternatively how great it is and then pick up another book to actually learn from

[graceful moon]

I feel like any introductory proofs, set theory or algebra book will discuss relations

But there also just isn’t that much to say about them

[heady ember]

Yeah, hence my remark about learning them as one goes

[vast jackal]

why is professor Leonard's video has some cut like some videos are deleted? 4.9 and 5.0 is not there?

[remote nova]

no clue

[narrow relic]

I would personally recommend you use other resources, I did not like that book. Chapters 1-5 are very well written but those are just on probability. The statistics part is much worse IMO.

[narrow relic]

I don't have any great recommendations off the top of my head but I remember thinking this book was better for statistics: https://onlinelibrary.wiley.com/doi/book/10.1002/9781118799635

Also, I'd recommend looking at lecture notes, a lot of those often deal with topics better than statistics books.

[pastel shale]

hmm okay thanks

gotta check out MIT OCW ig for any stats courses for their lecture notes

or do you have any in mind?

also, is the book you recommended intended for undergraduates or at a graduate level?

[dull smelt]

Best book for starting with formal logic?

[granite viper]

Is Apostol's calculus a good book to do after completing Stewart's calculus? Or are there other direction to go in?

[remote sparrow]

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

[hearty steppe]

It’s a good book but it’s definitely not like a first read for getting into theory heavy statistics or probability I would say… maybe after you work through a few texts… it’s a really tough read honestly

It’s a book I’m considering going back to after working through a few texts first

I like the exposition but I feel like I still need to work through other texts to be better prepared for it.

[remote sparrow]

https://www.reddit.com/r/math/comments/4jhag2/what_is_the_most_beautifully_written_math_book/

[lusty ermine]

top comment isnt math book

second one is ||concrete math by knuth et al|| and third ||is spivak?||

[fiery kraken]

Anyone got a good rec for linalg 1,2 ?

[tribal crow]

have you checked the pins?

[fiery kraken]

How can I see those?

[tribal crow]

#book-recommendations message

[digital lake]

It is a good book "Elements of the Differential ant Integral Calculus" by Granville for someone who is new to Calculus?

[narrow relic]

You can read this book without knowing any measure theory.

[pastel shale]

alr i appreciate it thanks

[pastel shale]

okay, thanks for the rec ill check it out

[orchid dust]

Anyone know if "how to improve your math skills" by Steve lakin is a good book?

[iron wolf]

"Fundamental Theorem of Calculus is left as an excercise for the reader" flashbacks

[remote vortex]

I think not even Rudin leaves the FTC as an exercise

[orchid dust]

I guess not?

[wary anchor]

Intro stats by velleman

[shadow vector]

D.J velleman?

[fervent marten]

ok but there should be like a simple and concise book about integration. any recomendations?

[remote sparrow]

...a calculus book?

"8th grader" is an arbitrary distinction here

if you want to actually do calculus, you should already have the background

and generally one has already covered limits and differentiation prior to integration

[fervent marten]

yes i just finished the ap calculus course in khan academy

[tribal crow]

then you have the background needed for any calculus book, imo

[fervent marten]

oh ok

thanks

[lusty ermine]

which book is good for multivariable

tangent planes and linear approximations

[remote sparrow]

what kind of book are you looking for

proof-based?

[lusty ermine]

yeah with rigurous rigurosity

[remote sparrow]

you can look at hubbard and hubbard or shifrin

[tribal crow]

look at Calculus on Manifolds too

(joking, but it doesn't seem half-bad tbh)

[remote sparrow]

it has a lot of errors from what i've heard

spivak supposedly speedran writing the book

think he wrote it when he was a grad student or whatever

[tribal crow]

yeah, I've heard this too

[halcyon arrow]

anyone got a good book recommendations for pre-calculus?

[tribal crow]

I'm trying to be wary of that

[remote sparrow]

you can probably google errata sheets on the web

[remote sparrow]

try Precalculus by axler

[tribal crow]

I have, actually

there's quite a few

thankfully

[remote sparrow]

or Basic Mathematics by lang

[abstract copper]

But Spivaks exercises are good, as I heard. Well, any multivariable analysis book has better exercises than Munkres' ones.

[tribal crow]

I've heard that Munkres' book has terrible exercises

[abstract copper]

I used Munkres' and most of the exercises aren't related to the contents, and also a lot of computational problem (like why??)

[halcyon arrow]

thanks

[abstract copper]

But at least he handhold you through proofs.

[remote sparrow]

imagine if copyright weren't a thing

take the exposition of munkres and the problems of spivak and put them together

[abstract copper]

Well it's not a thing if you don't get caught

[tribal crow]

I've heard that Hubbard and Hubbard is "the Munkres to Munkres"

lol

it is to Munkres what Munkres is to Spivak, supposedly?

[remote sparrow]

well it's supposed to be usable for honors multivariable calculus students that come straight from high school too

of course, the hard proofs that are left in the appendix aren't taught

[tribal crow]

I see

[remote sparrow]

but yeah it's usable for an analysis student as long as you look at the appendix

[heady ember]

Just use Schroder

[tribal crow]

Schroder is a nice book

[heady ember]

Gets you up to (and including) Stokes' Theorem

[tribal crow]

never got a chance to use it, but it looks really good

[heady ember]

Hi 🐟

[tribal crow]

so I've downloaded Hubbard and Hubbard to take a look (don't ask me how I did it): what's with all of these side remarks??

also, I'm in computational hell

[heady ember]

I like how he introduces the lebesgue measure fast af. Its nice to quickly get to learn about something you've heard so much about

[tribal crow]

what's with all that stuff on the left

it's jarring

[trail hemlock]

we don’t fuck w computations 💯💯

[tribal crow]

no wonder it's "the Munkres to Munkres"...

[heady ember]

Schroder encourages the reader to use a computer for computational exercises (namely, in chapter 13 of Numerical Methods)

[abstract copper]

Just multilinear algebra. I don't understand why he left the proof of Stokes to the appendix?

[tribal crow]

this is H&H

[heady ember]

Why the

[abstract copper]

Yes

[tribal crow]

ah

I'm just taking a look at it

and noting how... explicit it likes to be

[tribal crow]

seriously...

[heady ember]

Ah yes

[tribal crow]

what's with these paragraph remarks on the side 😭

[heady ember]

"Wtf is this, this is so ugly. Can't you make it more elegant?" The enraged fish asked.
"What is elegance" Hubbard asked, calmly?
"I dunno mate" The other Hubbard, replied, with his curiousity slightly piqued.

[tribal crow]

okay I'll stop posting huge images here

I'm just... very surprised

[heady ember]

Why fishy boi?

[tribal crow]

means nothing much

just that's I'm thinking

[heady ember]

I see

[tribal crow]

you can alternatively substitute a "hmm" message from me

but that takes space, so I use reaction instead

[heady ember]

hmm... fishy

[lusty ermine]

which reference has easy exercises for posets and hasse diagrams

[remote sparrow]

they're motivating remarks

again the audience isn't only very sophisticated students

[tribal crow]

wouldn't it be better to put them in the actual text then?

not all of them, just some of the really lengthy ones

[remote sparrow]

@misty wyvern Between Keener, Schervish, and Shao, whose treatment of measure-theoretic statistics do you prefer the most?

[remote sparrow]

in that world, you might have complained that hubbard was going on too many tangents in the main body of the text

[tribal crow]

fair enough, but I'm not really one to complain about exposition

I'm only complaining because putting so much on the side distracts me easily

[remote sparrow]

the text assumes no background in linear algebra

[tribal crow]

I see

it's trying to do a lot then

[remote sparrow]

it's a combined treatment of linear algebra and multivariable calculus

you can skim the linear algebra chapters if you already know it

[tribal crow]

I might consider referencing it as I read CoM then

thanks for the recc!

[remote sparrow]

👍

[misty wyvern]

If I had to teach a class I'd prefer Keener, Shao, then Schervish in that order.

It's worth noting that each of these books have results the others don't have so it's worth just glancing through them all at some point.

But Keener is probably the ideal lecture series.

[violet shuttle]

...like with a calculus textbook?

[marsh ingot]

Spivak?

Idk if talk about improper integrals

And I dont think you need Lebesgue theory to learn about it

Well.... nvm

[vocal owl]

Bruh

[gray gazelle]

dddue

[grave kindle]

Top 5 best books to learn algebra and geometry

??

[fiery kraken]

The bible

[frail pendant]

1. Lang
2. Hartshorne

[grave kindle]

💯 Guarantee

[grave kindle]

Thanks man

[graceful moon]

This man’s going to be the most cracked high schooler

We have created a prodigy

[round shore]

Embrace the 21th century

1. Ramero or Aluffi
2. Gortz Wedhorn

[frail pendant]

oh yes
https://pro.univ-lille.fr/fileadmin/user_upload/pages_pros/lorenzo_ramero/CoursAG.pdf

[graceful moon]

Just get him reading grothendieks original manuscripts

[round shore]

I added Aluffi because this one is only in French, but it's the best book ever

[lusty ermine]

which book is good for grabbing elementary number theory info

[glad rampart]

I like AoPS intro to number theory

[fresh skiff]

I accidentally downloaded it and opened it
Oh my gosh! AG in French.. both are far away from my understanding

[gray gazelle]

Ireland & Rosen if you’re comfortable with proof writing already

[fresh skiff]

Do you mean that GTM book?

[gray gazelle]

Yeah

[fresh skiff]

Oh I have read almost chapter 3 from velleman and chapter 2 from abbott. And know some Number theory.
What do you think, is it enough background

[gray gazelle]

For I & R? Yeah, the first 6 chapters can be read with essentially no background, and the first 10 with minimal supplemental (algebra) reading. After that, you’d need more background in algebra, as well as some complex analysis for certain chapters

[fresh skiff]

That's surprising. Usually GTM book required some background. I will read this book (online) and check if i am comfortable

[gray gazelle]

What would be the best calculation collection you recommend?

[gray jungle]

whats do you mean by "calculation collection", what kind?

[gray gazelle]

calc 1, 2, 3 and 4

sorry for my english

[lusty ermine]

how to improve graph theory machinery,, any references

[gray gazelle]

Diestel is pretty standard

[hallow oriole]

diestel is standard but im not convinced it's the best

[narrow relic]

Schervish is a good book for Bayesian statistics, I have used some sections. I'm not sure I would read it all in sequence

[graceful moon]

Wilson’s a book is decent, not amazing but for a concise introduction it’s the best I’ve seen (5th edition anyway, better than the older ones)

[lusty ermine]

Any references for elementary measure theory

[deep moat]

Scale of 1 - 10 aops

They're very good books

[marsh ingot]

Bartle

[remote sparrow]

https://measure.axler.net

[dapper inlet]

ive been using david lays book but it doesnt have a chapter on isomorphisms

where can i find an equivalent

[remote sparrow]

#book-recommendations message

meckes or hefferon are your best bet

[gray gazelle]

Does anyone have any good textbook reccomendations on functions? wanna get prepared starting from summer 😄

[narrow relic]

What do you mean on functions?

[daring lake]

Functional analysis ofc

[left saddle]

the things that happen when you press the buttons ya know

[mossy flume]

khan academy tbh

[feral verge]

if you prefer reading, mathisfun.com is great. Because it's written, you can glance over what you already know. It provides tons of examples and explanations to get the point across. Here is a page on algebraic functions https://www.mathsisfun.com/sets/function.html, if thats what you're asking for; otherwise, here are all function related pages: https://www.mathsisfun.com/search/search.html?query=functions#ff

[arctic mist]

Anyone have any recommendations for set theory and ergodic theory that can help lay groundwork for stuff like QM and QED?
My background is EE, and I'm getting more into physics but I don't really understand the math past a post-undergrad/early-grad level of real/complex analysis and Linear algebra

[gray gazelle]

ty 😊

[golden salmon]

ergodic theory for physics is a hardcore way to do it. If you've got an EE background may I suggest "A Course in Modern Mathematical Physics" by P. Szekeres. If you're in uni you may be able to get free access via the cambridge page: https://www.cambridge.org/core/books/course-in-modern-mathematical-physics/E899DB30C574E2F4D7C861B3097F9813

[lusty ermine]

Pde reference book?

[lusty ermine]

is it ok if I keep reading although I dont undestand all the details?

[vast jackal]

yes and read them back so you can understand them better

remember math isn't always about that topic it has other topics also.

just got it from lang's foreword

[gray gazelle]

is aops something you have to read the whole collection, I just picked up the intermediate algebra but it seems like they teach a certain way of problem solving that kind of goes over your head if you just read one of the books

[pine vault]

anyone know where I can find a good explaantion on recurrence relations/tree problems?

[lusty ermine]

Im curious about this aswell, please let me know if you find any references

which discrete structures book to follow?

[tribal crow]

imo, you can just skip it if you've done such a course before

[hearty steppe]

I'm having trouble engaging with Ergodic Theory texts myself... Do you feel this book proposes a better angle to understand Ergodic Theory outside of general dynamical systems texts that just touch the surface?

I think the right physicist or mathematician that decides to make a more digestible Ergodic Theory text will become super famous in the near future 🤣

seriously the books I've found are DENSE as all hell and too full of esoteric rigor to meaningfully work through.

Maybe I should just work through the stat mech books I've been recommended and I'll just develop an understanding of ergodic theory through the principles of entropy

[abstract copper]

The prereq to ergodic theory is measure theory, no?

[hearty steppe]

Not exactly?

Measure theory is a nice general way to develop an angle to approach ergodic theory... much like how it helps with understanding probability theory

I recommend the measure theory route personally... I think the biggest important areas of mathematics right now probably are measure theory, representation theory, and category theory...

Combinatorics is important as well but builds on these IMO

[abstract copper]

Yeah I'm currently studying measure theory. I'll get to ergodic theory someday perhaps

[hearty steppe]

Like a way one can generalize what ergodic theory is... is a patternized behavior that happens over some period of time... generally long term as opposed to short term... when we consider symmetry breaking.

but measures help us generalize intervals of the patternizations per se

I'd say it is a prereq angle but... from my experience it doesn't quite get you to ergodic theory intuitively... Maybe if you really can wrap your head fully around formal rigor in measure theory then I am wrong about that... but there is so much happening in measure theory... I cannot say I can fully understand it myself despite how many times I work through books I enjoy.

representation theory is another area I'm really struggling with... but I think working more on group theory is going to get me there... so I'm considering working through more linear and abstract algebra texts

but measure theory has been mostly comprehensible to me... depending on the book I choose to work through. I really enjoy Folland's real analysis even though I didn't fully understand it. Going through Billingsley's probability and measure right now

I think everyone should read Folland's real analysis. It's probably my favorite math book ever

[abstract copper]

I'm currently using Axlers supplemented by Folland and it has been pretty gentle so far.

[hearty steppe]

I hear great things about Axler's measure theory text and its certainly on my reading list. A number of people told me don't worry about the linear algebra text he gets a bad rap for... his measure theory text makes up for it

I mean so far... general measure theory texts I've read have been comprehensible to me... but I do my research on them before I read them.

[abstract copper]

His linear algebra gets a bad rep? Most people either will love it or hate it, as evident from this discord lol

[hearty steppe]

Also disclaimer... I'm not a mathematician or physicist and neither am I trying to become one... I'm quite stupid at maths and physics compared to the people frequenting this server

[abstract copper]

Most of us are...

[hearty steppe]

the books recommended to me have been inspiring for my work and I love the frequenters here for their input... even if its sometimes a little bit on the rough side like a tough love sort of thing.

Mods have been great and I generally really love the textbook recommendations I get here... hence why I keep coming back 🙂

[marsh blaze]

Anyone know of some good books on fourier analysis?

[jade stirrup]

What book should I get to teach proofs and logic? I've been wondering if there was one which starts with the fundamentals of logic, as well as sets, and then slowly build it up and then show how mathematical proofs work and how you can mathematically prove things as well

[bright epoch]

people are going to disagree with me here but I really liked Proofs from THE BOOK

How to Solve It by Polya was also good, but I read it well past when I needed it so idk if it's actually good or if I just enjoyed it

[jade stirrup]

I see. Thank you

[bright epoch]

another thing; logic, sets, and proofs are kinda three seperate things

[heady ember]

You can't do set theory and logic without proofs tho?

Set theory and logic are also quite interconnected I believe

[bright epoch]

there are connections, but none of the books I sent are on logic or set theory, and texts on set theory or logic are not at all guarenteed to include the other

[karmic tangle]

Has anyone here read "Conceptual Mathematics" by Lawvere and Schanuel?

The reviews on it seem to be quite polarizing

I've started reading "Algebra: Chapter 0" by Aluffi and "An Invitation to General Algebra and Universal Constructions" by Bergman and I was thinking that maybe while I'm reading those I could also pick up said book too

I'd like to eventually read Goldblatt's "Topoi" and Lawvere's "Sets for Mathematics" and I thought this could be a good stepping stone (since it's supposedly the least technical/advanced text on such topics, surely it would just make it easier to then go into these two, right?)

[cold tusk]

Any books on set theory?

[karmic tangle]

I've heard Thomas Jech's is a/"the?" classic but I can't say anything about it personally because I have no clue

probably more of an encyclopedia than an introduction

[cold tusk]

I’ll look more into it thank you!

[karmic tangle]

are you looking for an introduction

[gray gazelle]

Naive Set Theory is a good first book

And it has a dover edition

[karmic tangle]

I just wouldn't want you to be losing time with some needlessly big book (it's nearly 800 pages lol), it was recommended to us by our Set theory seminar teacher but I think his perspective is a bit different than that of someone looking to get into the topic XD

[heady ember]

Sure but you said they were separate things, which was what I was addressing.

[heady ember]

What leve of set theory are you looking for? Naive? Axiomatic?

[heady ember]

Yeah it is

BIg Jech is for grad level set theory

[cold tusk]

I have no clue what any of that means, I’m a high schooler with the latest math I’ve done being trigonometry, I want a PhD in CS though, so I want to learn math plus I enjoy math so

[karmic tangle]

Naive Set Theory was good but all the definitions/statements are super wordy - I guess it's because of the time it was written but I had trouble with some of them when what could be said with a few VxE f : A -> B: ... type expressions was instead a rather long strudel of "every x for which ... for which such that ... such that there exists an _ which..."

[heady ember]

Even then, normally people learn from an easier book before going to Jech.

[gray gazelle]

Rather than learning set theory on its own, you’d be better off working through a discrete math book, e.g. Concrete Mathematics by Knuth

[cold tusk]

Okay I will do that appreciate you guys!

[cold tusk]

Oh and, how would you go through the book personally? Is there anything I can do to supplement my reading? I dont exactly enjoy taking notes but if I have too and if you recommend it I will

[gray gazelle]

You should try to prove all of the results before reading the books proof, then compare your solutions

Do all of the exercises

Look at the ideas from several angles: from the formal, to the intuitive, and back again

[cold tusk]

Are the solutions to the back of the book? The solutions aren’t on the same page as the exercises right?

[karmic tangle]

Also if you get stuck on an exercise sometimes doing another activity for a while then coming back to it helps

[cold tusk]

Haha I learned this like crazy from programming, can’t solve it today? Come back later

[karmic tangle]

yeah exactly, you could also look at the other exercises and see if you can do some of them in the meantime but make a note of the exercise you hadn't solved so that you really come back to it

you can look at the pdf right now to see what the book looks like

[gray gazelle]

I think Concrete Math has solutions to some of the problems

One sec…

[karmic tangle]

idk about this specific one but in pretty much all the cases the solutions aren't on the same page I'd say, in these types of math books

[cold tusk]

I see okay okay

Does discreate maths require creativity?

[karmic tangle]

if you like programming I think it'll be a good fit

[gray gazelle]

Ok yes, yes they do

[gray gazelle]

Yes

[cold tusk]

I’m done for

[gray gazelle]

You’ll need to work on your creativity at some point lol

That’s basically what a PhD in CS entails

[cold tusk]

I mean I guess Im downplaying my creativity, I am good at coming to with solutions for programming, fairly quick too but it’s not always the most efficient, I’d have to come back later and refactor

I think I’ll be fine (I’m coping)

[cold tusk]

True, it’s 95% theory no? Programming is applied computer science basically 😭

[gray gazelle]

You get better by practice

[hallow oriole]

to learn proofs?

yeah you're wrong 😭

[bright epoch]

see everyone says this but it was my first proof based book and I loved it

[hallow oriole]

that's mildly obscene

[bright epoch]

yes I'm aware lol

[hallow oriole]

im glad it worked out (?) for you but i would never recommend it to anyone else

seems like a truly awful experience

[spiral raft]

differential equations book?

[bright epoch]

PDEs or ODEs

[golden salmon]

It's not an ergodic theory book, its a book that builds up the mathematics used for qm and some of whats needed for QED. The only times I've seen ergodics turn up in physics is either in a statistical physics context (many body systems) or a classical dynamics context (chaotic systems). Though ymmv

[bleak canopy]

any book recommendations for learning ordinary differential equations and multivariable calculus? I want to get a head start on it for my second year of university

[remote sparrow]

do you want a proof-based book

[bleak canopy]

for now, no

just something with a lot of compuations and practice problems

[remote sparrow]

do you still have your calculus book? one of those big ones like stewart or larson. it should cover some multivariable calculus. as far as ODEs go, see here: #book-recommendations message

[bleak canopy]

thanks

i do have my original textbook

but i wanted to learn from a different one

[remote sparrow]

is there a reason why you dislike your calculus textbook? most calculus books are pretty similar to each other, so if you don't like your calculus textbook, chances are you won't really like others

[bleak canopy]

it's not that i dislike that calculus textbook

i just wanted something different

[remote sparrow]

well i would recommend you save your money

[bleak canopy]

i wouldn't be paying

i can easily find it online

[karmic tangle]

lol

we had a course where the whole of it was just each person choosing one proof from Proofs from THE BOOK and presenting it

it was interesting but also very confusing XDD especially in a CS program where there weren't that many other proof-based courses (unless one took them as electives)

thankfully I was the first to present so I was allowed some leeway to choose a simple proof

anyway I feel like the book isn't a good thing to show to someone who hasn't already had at least a bunch of proof-based math courses and even then things just make so much more sense in the context of an actual book/course on said topic than as "wow look at this out of context cool proof from one part of math"

well it can be motivating I guess

[lusty ermine]

how to get into modular arithmetic

I want to understand little theorem of fermat

for prime nums

and I want to explore divisibility of numbers

any references that ring a bell for this?

[bleak canopy]

i'd recommend just picking up any number theory book

they all cover modular arithmetic even within the first few chapters

[lusty ermine]

what did you pick up for number theory?

[bleak canopy]

i never learned much number theory

and i never learned from a textbook\

but from what I see online a classic example

would be

An Introduction to the Theory of Numbers, by G. H. Hardy and Edward M. Wright

i've skimmed the first few bits of it in the past it's alright i guess

[past dust]

How’s the book Calculus: Early transcendentals ? Is it good ?

[ancient sand]

hey where did you get that pfp

[bleak canopy]

it's a selfie?

i'm miyamoto musashi

[ancient sand]

Lol

i only ask because i know someone with the same pfp and was curious

[bleak canopy]

why tf they have a photo of me

[ancient sand]

stalker

how'd you become immortal

mercury or what

[vast jackal]

what do you do when reading proofs?

[glad rampart]

Read them

[hallow oriole]

depends on the level of the proof

if it's something i've seen or done before, or if it's just simple, not that long. just check over it. if it's at the level i'm at, maybe an hour of study, playing around with examples, checking where the conditions are used in the proof, etc. if it's above my level, occasionally weeks of studying and staring and studying supplementary and similar material

these are all like really variable

some proofs can take minutes, some can take hours, some can take days

etc

[vast jackal]

i thought you will reconstruct them on your way like changing it lol but sure that's what i do also

[violet shuttle]

My main bottleneck when reading proofs is that I encounter a statement/step whose justification is incomplete (this is not necessarily a bad thing on the part of the author). At this point I do the same thing I do when trying to solve any mathematical problem

Afterwards is the "compression" step

like "oh this first paragraph is just [bla]"

or creating intuition

or working through an example

etc.

[glad rampart]

Makes sense

[fresh skiff]

The interesting part to read theorem and its proof is to find counter examples when some hypothesis is dropped.

[vast jackal]

what are some parts in basic mathematics that are theorems?

[round shore]

What do you mean ?

[vast jackal]

idk never know what a theorem is

[pastel shale]

a theorem in math is a statement that has been proved true

Pythagorean theorem is a basic one

[vast jackal]

oh like if a+b = 0 then a = - b b= - a?

to prove that

minus a to both side to get b = -a

[gray gazelle]

yeah, theorem just means “true statement”

[vast jackal]

oh i alr understand theorems

[pastel shale]

im not that familiar with higher level math but i think messing with variables like that analytically is built off of other proved statements

you go very deep like proving anything + 0 = anything and stuff like that, you go even lower

[gray gazelle]

Not really

What you just wrote is essentially the definition of 0

[pastel shale]

ah ok

guess there are other examples tho idk

i was referring to this game i was playing that used lean to prove statements about the natural numbers

very eye opening how we take for granted basic operations

[vast jackal]

the proofs in basic mathematics are simple but idk in the next chapt lol

[pastel shale]

is "basic mathematics" a book or are you just saying in general?

if its the book by Serge Lang, ive never read it but just looking at the topics it seems like algebra/precalculus, so nothing conceptually difficult it just takes time and practice to learn if you're doing it for the first time

although idk if i have the right book they teach a bit of linear algebra and other stuff so that might get a bit harder if you've never seen it before

[vast jackal]

a book

[languid portal]

What’s a good book on PDEs?

[graceful moon]

I’ve seen Taylor recommended here a few times

I know that there’s one guy who does PDEs that really likes those books

[round shore]

Evans

[hallow oriole]

probably @glad prairie

does anyone else here actually do pdes?

[tribal crow]

Delerik…

I’m pretty sure Delerik is the one who recommends Taylor

his username is literally Delerik_taylorpilled

[heady ember]

Hi fishy boi

🐟

[tribal crow]

hai

[slim crescent]

anyone know a good stats book primarily for the purpose for CS

[graceful moon]

I was referring to delerik but I didn’t see any reason to name drop him lol

[glad prairie]

I dont really have a favorite pde book

[hallow oriole]

ive never heard of this person in my life

[hallow oriole]

but somehow u have opinions on everything else........

i kind of want to know what ur math book tier list looks like actually

send

[glad prairie]

I dont like math books

I like like 3 math books

Well, ok i probably like more

[deep nebula]

how do you all stay motivated to read a book? i do have some motivation, but it is almost always messed up by distraction and procrastination.

like right now, i should be reading a book, but i am looking for advice instead.

[tribal crow]

I’ve been wondering the same thing lately haha

[deep nebula]

and even if i start, i will be distracted by say, a new youtube video by pbs.

[vast jackal]

number 1 don't search for an alternative
number 2 ask help don't look for an alternative
number 3 delete useless apps
number 4 what's your reason to study
number 5 consistency even if it's a small progress lol

[shadow vector]

Afaik theorems are formulas that can be derived from no premises. That is either from a set of axioms and inference rules, or purely a set of inference rules and no axioms (consider a natural deduction proof system that needs no axioms). A theorem is therefore a syntactical notion, of a string of symbols in a language that the syntax makes special in some way. Theorems are the syntactical analogue to the semantic concept of tautologies, which are formulas which are satisfied in every structure (true in every interpretation).

Just to add this then, soundness is then that every theorem is a tautology and completeness , that every tautology is a theorem.

but maybe thats not really what you were asking... idk

[remote sparrow]

i doubt klaus was even thinking of mathematical logic when he wrote that

[shadow vector]

ah, my bad then

[shadow vector]

oh yeah, i was more so responding to silvers comment

a theorem in math is a statement that has been proved true

[fresh skiff]

Any recommendation for mathematical logic for beginners?

[remote sparrow]

#book-recommendations message

if you have no algebra background, i would avoid mileti as he makes extensive use of algebraic examples

leary and kristiansen is the most accessible

[fresh skiff]

Sorry, are you talking about abstract and linear algebra or school level algebra?

[remote sparrow]

abstract algebra

[fresh skiff]

Oh i understood. Lemme check leary and kristiansen. Thank you

[remote sparrow]

https://knightscholar.geneseo.edu/cgi/viewcontent.cgi?article=1005&context=geneseo-authors

[fresh skiff]

Thank you so much for the pdf.

[shadow vector]

DOING logic in the context of mathematics? Id recommend D. J. Vellemans "How to prove it".

For understanding the underlying workings a bit better probably just the open logic text

i can send pdfs for both

cant link here apparently

[fresh skiff]

Ah I did 1,2, ½3 chapters from velleman

But curious to know what formal logic

[shadow vector]

what formal logic?

oh

yeah, so for that i would recommend the open logic text /texts. https://builds.openlogicproject.org/

you can download the complete pdf or the singular texts. Its the same content either way

[fresh skiff]

Almost 1000 pages wow

Seems a good reference book. Thank you so much

Btw it is a random question, does there exist such comprehensive notes/pdf for real analysis too?

[shadow vector]

Yeah, the complete book like i said is just a collection of all chapters from the other books., Its not practical to work through, but you can just go to the specific topic to look through it

[shadow vector]

Dont know unfortunately sorry 😅

OH wait, it says in my role that im a "Pending Postgraduate" Thats NOT true! Where can i change that??

[fresh skiff]

Ikr. The author stated the same fact that this using this pdf as a textbook isn't a good idea.

[fresh skiff]

No worries 😅. Thank you so much for your time

[fresh skiff]

Go to the channels section in the starting of the server

Channels and roles

Ig there you can change.

[shadow vector]

if i change it i lose access to a lot of channels

[fresh skiff]

Oh. In this case idk anything. Sorry

[shadow vector]

nvm im dumb, i fixed it!

[orchid echo]

I really enjoyed the book by Ebbinghaus for mathematical logic

A friendly introduction is also quite good

But it’s a bit terse

[stark turret]

not math but what is a good book for circuit and schematic design

is Leonard Bobrow’s “Elementary Linear Circuit Analysis” any good? (I know it’s a good book but idk if it is good for specifically what Im looking for)(

[cold tusk]

Can someone recommend me a discrete maths book that’s a bit lighter than Concrete mathematics..

[cold tusk]

I think I’ll use this: https://discrete.openmathbooks.org/dmoi3/preface-2.html

Then come back to concrete mathematics lol

[sturdy shore]

any discrete math book you'll find is gonna be easier than concrete math

I guess Rosen is standard

[cold tusk]

Why is it always recommended first then, I’m telling you this book has ruined my self esteem and now I feel like I’ll never be good at math

😭😭😭

[glad rampart]

Sounds like an issue with your mindset, not the book

[sturdy shore]

is it always recommended first? I rarely see that book recommended at all, to be honest

[cold tusk]

Changing my mindset won’t make me smarter unfortunately, my mindset was perfectly fine until this book almost murdered me

[remote sparrow]

i'd wager that people passionate and who have worked very hard at math are more likely to be on online spaces about math, and thus recommend books that are more challenging for the average reader

[sturdy shore]

everyone encounters books that are too difficult for them at some point, you aren't unique

[glad rampart]

Clearly it wasn’t very good if some pieces of paper was enough to disrupt it

[cold tusk]

I felt like I was missing a lot of stuff I was suppose to know BEFORE diving into the book, someone later informed it it assumes you know formal logic, and some other stuff

[remote sparrow]

you do not need to know formal logic

truth tables are not formal logic

[sturdy shore]

From what parts I've read of that book, I don't think you need logic

it's just a difficult book

[cold tusk]

The book is hard, that’s the gist of it, everyone’s felt some way after encountering something is hard, if I thought it was the end of the world I would have given up on math already, I don’t lol

That’s why I asked for another book, and that I would come back later

[cold tusk]

I thought so, I didn’t expect it to be easy, but I also didn’t expect it to be as hard as I find it, maybe I’ll try giving it another read tomorrow

[glad rampart]

I’d recommend an intro to proofs book personally

It seems like that’s something that would help

[cold tusk]

What do you recommend specifically?

That’s a good intro

[remote sparrow]

discrete math books are already supposed to be intros to proofs but written with a CS student in mind

[sturdy shore]

yeah, but I don't think concrete math is like that, all the reason he shouldn't be using it

[glad rampart]

I learned proofs with the AoPS books but that might be a bit long just to learn proofs

[remote sparrow]

maybe for a cracked student (or an old school student like the math sorcerer)

he made a video mentioning he was assigned this book

[sturdy shore]

it's always different when there is a prof handholding you

[cold tusk]

The art of problem solving?

[glad rampart]

Yeah

I’ve worked through 4 of their books

Working on a 5th

[cold tusk]

It has exercises in it?

[glad rampart]

Yes

[hallow oriole]

just use book of proof if you need to learn proofs

https://www.people.vcu.edu/~rhammack/BookOfProof/Main.pdf

u got this and gl

[cold tusk]

What the other person recommended or what you recommended? Or it doesn’t matter just pick one?

[cold tusk]

This looks nice and has exercises

[sturdy shore]

I haven't read any AoPS book, but I do know that 1 book suffices to learn proofs

[glad rampart]

I haven’t read the book of proof so I wouldn’t know

Yeah

If it’s good I’d recommend book of proof

[sturdy shore]

and book of proof is great

[glad rampart]

I did AoPS mainly to learn the material and it taught me proofs along the way

[sturdy shore]

afaik AoPS is supposed to be like a long term project for very young people to progress in a long period

[hallow oriole]

also, aradia, i've kind of come around to aops

[glad rampart]

Yeah

Although I’m getting through it pretty quick lol

[hallow oriole]

i still think the combinatorics book is not good, but i looked at the others and they aren't bad at all

so im sorry for disagreeing w u on the nt stuff

[glad rampart]

Mhm

[cold tusk]

Okay I’ll just go with it, and I’ll update all of you on my progress and ask for help here, and I’ll try to make my mindset bullet proof like you said

[glad rampart]

I still liked the combinatorics book personally

[hallow oriole]

yeah it's just that it's not an intro to combinatorics

it's more an intro to olympiad combinatorics

it's a great book for that purpose ofc

[glad rampart]

I mean imo it still serves as about a solid of an intro to combinatorics as could reasonably be expected for a book targeted towards middle and high school students

Introduces many important things

And it’s nice for probability as well

I prefer the probability section tbh

Feels like the combinatorics one was mostly setup for probability

[hallow oriole]

it's fine for intro prob, sure

i'm just against calling it an intro to combinatorics

the first four chapters of walk through combinatorics covers most of the combo in the book better and i think a few of the later chapters are also accessible to hs students

[glad rampart]

Fair

I can’t speak on that having not read that book

[hallow oriole]

if you enjoy what you've done so far maybe give it a shot

it'll be quite different though, especially as you get further in

[tribal crow]

@hallow oriole what would be your recommendations for combinatorics?

I know you study a lot of it, so I was wondering if there's smth you recommend

(I may or may not learn combo one day)

[hallow oriole]

for intro read a walk through combinatorics by bona and supplement it with bijective combinatorics by loehr. from there it kind of depends on what you want to do first

if you know algebra probably stanley's algebraic combinatorics

or a graph theory book

[tribal crow]

[glad rampart]

The intermediate combo/probability one from AoPS covers a bit of graph theory iirc

Idk how you feel abt that one

[hallow oriole]

i like some of the treatments they use but it's not as comprehensive as i'd like

not a big issue, though

[glad rampart]

Cool

I’ll probably check out that one and maybe some of the combo books you recommend if I have time before college lol

[hallow oriole]

go for it!

but don't overwork yourself

you have time

[glad rampart]

Yeah

[marsh blaze]

Any recommendations on a book about Fourier analysis?

[fresh skiff]

Fourier Analysis by Elias Stein is standard one (but I haven't read it yet bcz of the lack of prerequisites)

[marsh blaze]

Thank you : )

[gray gazelle]

What are the prequisites

[fresh skiff]

Riemann integration.
For more discussion on prerequisites see
#book-recommendations message

And I am on chapter 2 of abbott. Riemann integration is 7th chapter ig. So it will take me a good amount of time to pick that book

[hallow oriole]

you'll want to know linalg too

[tribal crow]

I see LA, I am summoned

[fresh skiff]

Ooh. I have some experience with linear algebra.
Like vector spaces, inner product spaces, basis, span, linear transformation etc
But i am less familiar with proofs in LA .

[tribal crow]

you can check the pins for a review of many proof based LA books

[fresh skiff]

Oh yes. Just looked at them rn.
I will pick LA after real analysis.

[tribal crow]

I hope you find it more enjoyable

(this is just me projecting, ngl)

[fresh skiff]

hopefully thank you!

[sage python]

You don't like linear algebra???

[sage python]

That is a thing one does in linear algebra tru

[strange owl]

What is a calculus book that good for self learners

[tribal crow]

other way around

I really hate real analysis lol

I adore LA

Afzal said that he'll pick up LA after RA, to which I replied "I hope you find it more enjoyable"

[sage python]

Oh oh

Lol

Real analysis can be good fun too tho

[tribal crow]

I had a terrible time with it in my first few months, to the point of almost dropping math entirely

[sage python]

But yeah at first I interpreted it as "I hope you enjoy linear algebra more than I did" and I was like :0

[tribal crow]

I did come around to respecting it though

in retrospect, it wasn't that bad, but I harbor bad feelings about it still lmao

on the other hand... I've found LA to be just about the most interesting thing there is

[heady ember]

Why

[tribal crow]

see what I said below that

[heady ember]

Yes I saw that. But what were those terrible experiences?

[haughty igloo]

I really enjoyed LA too. Something about manipulating structures is beautiful

[magic moth]

any recommendations for a operations research book that is not Lieberman?

[past dust]

How’s the book Calculus: Early transcendentals ? Is it good ?

[graceful moon]

Presuming that you mean James Stewart’s book, it’s the standard calculus book in a lot if not most places so yeah pretty solid

[past dust]

yep James Stewart's book, is it good for self studying ?

[gray gazelle]

Definitely recommend it fr💀

Bro is on top of his class after this

[remote vortex]

This is clearly a joke, but just to avoid misleading innocent people: Rudin's PMA is a terrible book for self-learners.

It's a great reference book for people familiar with the subject, and it's just about acceptable in a guided course.

But studying from Rudin on your own is really not a good idea for most people.

I did say most people. There are some Rudin success stories, but they're few and far between.

[heady ember]

Enderton was harder than Rudin. Fight me.

[remote vortex]

Ruding being horrible doesn't mean it's the worst, I'm not going to do rankings here

[heady ember]

I'm just joking

Enderton was probably hard due to my mathematical inmaturity

[graceful moon]

Yes Stewart is great for self learning, full of easy (harder ones too of course) problems and examples and it goes at a much slower pace than some other books

[vapid pawn]

anyone have recommendations for linear algebra? I finished up to multivariable calc but i see a lot of negative opinions on axler, so i was wondering what people recommend for beginners, or should i just use mit ocw or both? And just curious what book would be cool for further study into linear algebra (maybe I will look into it to)

[graceful moon]

I’d go so far as to say the book basically feels like it was designed for self study

[past dust]

that's good to hear, thanks!

[violet shuttle]

eh

it's fine for exactly past me

i just can't in good conscious recommend a book that probably will be worse for most without adding the explicit cavest

[graceful moon]

What are your goals? If you’re planning to purse like pure maths then something like Hoffman Kunze is good, a lot people do like Axler (I don’t, but people do), there’s a few more recommendations in the pinned comments of this channel

If you’re not as pure maths focused I think nicholsons linear algebra book is good, it bridges the gap between just computations and theory well imo. People also like Strangs book, plus there’s online lectures to go along with that

#book-recommendations message

There’s a review by one of the mods, all his opinions of course

[vapid pawn]

Well it’s both for testing out of linear algebra but also just cause math is cool lol. Which is why I said i might look into studying linear algebra more, idk. It just seems like there’s a whole lot of stuff i will miss out on just Taking linear algebra once and that’s it. But thank you.

So far I don’t mind pure math I think, I enjoyed proof exercises in calc alot

[hallow oriole]

this but unironically!!!

i am convinced that if enderton was marketed as a cure for insomnia he'd be a billionaire

[heady ember]

Are you referring to his set theory book?

[hallow oriole]

yes

[heady ember]

Oh I see

I always assumed it was my skill issue

which it probably was

[hallow oriole]

probably 😭 me too

but i maintain that it was still unbearably boring

[heady ember]

Tbf he has some comedy in ch 3. Suddently AC appears

[heady ember]

I wasn't really bored, though tbf that was the first math book I read (so naturally everything was relatively new and exciting).

Once you get into the chapters on cardinals and ordinals that's where the best stuff is at iirc

[karmic turret]

yo,anyone has the resource about solid geometry?

[hallow oriole]

oh, interesting

[karmic turret]

our teacher's homework is hard AF

[hallow oriole]

it unironically makes me fall asleep when i read it tho 😭

it's just something about his style

[karmic turret]

completely dunno what the problem is sayin

[hallow oriole]

it's so dry it makes me feel downright dessicated

[heady ember]

You won't fall asleep trying to prove every theorem

[hallow oriole]

i feel like writing elementary set theory proofs is one of the Five Great Torture Methods of Mathematics

up there with talking to hscts and talking to collatz cranks

[glossy zealot]

I guess one of the other five is writing matrices

[heady ember]

I would disagree. Proving the equivalency of the various forms of AC was pretty fun

Never quite managed to prove Tarski's Theorem about Choice, but was still fun thinking about it.

[hallow oriole]

oh, that kind of proof

sure fair

the vast majority of the exercises are nowhere near as interesting

[heady ember]

Depends on which part of the book you're at I suppose

That's also one reason I try to prove all theorems myself

Some of them are quite interesting and thought-provoking

in a nice way

[glossy zealot]

Guys which undergrad real analysis books have decent mid-level difficulty problem sets?

[hallow oriole]

abbott, maybe

[heady ember]

Ah this reminds me. In other set theory texts you'll use class functions. But Enderton does it the full formal way, so you'll be using predicates throughout. Not a bad thing for a first exposure though, imo.

[hallow oriole]

or the easy exercises out of rudin

[heady ember]

Rudin, unironically.

Though depends on what you mean by mid-level

[hallow oriole]

i don't disagree, per se, but it def isnt for everyone

[glossy zealot]

I consider rudin to be one of the more difficult

[heady ember]

Yeah sure

I don't think I've encountered anything in Rudin yet that was quite as difficult as the most difficult parts of Enderton, three chapters in.

[hallow oriole]

yeah i think rudin difficulty is exaggerated if you have a good proof foundation already

[heady ember]

Yeah

Baire's theorem was pretty fun to prove

[hallow oriole]

im still not convinced it's the best book to learn from but it's not too bad

[heady ember]

The topology proofs have been a joy to complete.

[hallow oriole]

enjoying topology will serve u well

[heady ember]

There are nontrivial proofs, but they also have nice intuitions to arrive at. I never really felt truely stuck in that I had no idea on how to even think about the theorem/question. I think this was why I enjoyed the topology stuff a lot.

[glossy zealot]

Ok thanks guys i will add them to the list for this summer

[heady ember]

Have fun!

[trail hemlock]

u did question 22?

yeah it was a nice problem but it took me way to long to solve

[remote vortex]

Yes, but I'd say you're at an uncommon level of mathematical maturity compared to most people looking for a calculus textbook

In particular you're familiar with how mathematical proofs tend to go

[trail hemlock]

problem 19 was nice too

[trail hemlock]

basically, grass is a nerd .

[heady ember]

It was to this message

Guys which undergrad real analysis books have decent mid-level difficulty problem sets?
that I replied
Rudin, unironically.
I definitely wouldn't rec Rudin to someone looking to learn calc

[heady ember]

Yeah #1193952829191237633 message

[trail hemlock]

yess it’s so nice

oh u did it way diff than i did

[remote vortex]

Yep, Rudin is a fine book in terms of problems

[drowsy thicket]

Did you solve everything up till chapter 3?

[drowsy thicket]

No access

[trail hemlock]

it’s the top secret feet pics channel

[drowsy thicket]

what

[trail hemlock]

nvm 🙄

[drowsy thicket]

Do you not have access to it either?

[trail hemlock]

it’s a server for the rudin reading group

[drowsy thicket]

Ah

[drowsy thicket]

Did grass work out the problem there or was there discussion about it?

[trail hemlock]

grass solved it

just ask him to send his solution here

idt it’s top secret

[remote vortex]

Dangerous knowledge

[fresh skiff]

Recently I have seen, frequently chat is about baby Rudin.
After hearing all I have made a road map

Abbott (reference : spivik, ross maybe, Cumming) --> Axler (measure theory) and Fourier Analysis (stain) --> baby rudin

[trail hemlock]

grassian wisdom

[drowsy thicket]

I was just curious about how that server works, do you just work out stuff yourself and send it in there?

[heady ember]

Nope. I did the exercises assigned as hw and some that I found interesting.

Was stuck on proving that all perfect subsets of R^k are uncountable, and on another exercise. Should probably revisit those when I'm free.

[heady ember]

Approved by Eric

[heady ember]

We submit the hw exercises assigned. But because the instructors have been busy, we haven't gotten them back yet.

I post my solutions there, especially when they are not part of the hws. Then DarQ or Eric normally help me check it

Also uh we're getting off topic.

[drowsy thicket]

Ah, alright

[bitter summit]

\mathfrak g not a lie algebra moment

[trail hemlock]

grass do 19 🥺🥺

[iron crest]

Is GTM9 a proper introductory book about lie algebras?

[remote sparrow]

#book-recommendations message

[shell geyser]

thoughts on "towards higher mathematics" by richard earl?

[vast jackal]

hey i have a question

the theorem is like the solved case of math/solved mathematical statement which is proved by proof. While a proof is a process to prove a mathematical statement which if solved will become a theorem? am i right?

[drowsy thicket]

Was stuck on proving that all perfect subsets of R^k are uncountable, and on another exercise. Should probably revisit those when I'm free.

Do you generally not ask on this server when stuck on something?

[remote vortex]

Amusingly, Baire's theorem can be used to prove that quite easily (although I think Rudin's proof doesn't use it)

[still panther]

How? i only know about the proof that injects Cantor space into the perfect set

I guess uhh

we can say that the perfect set being closed admits a complete metric and if it was countable it would be isomorphic to Q which we know does not admit a complete metric because it is not a G_delta set in R?

but does not strike me as easy so you probably have something else in mind

[gray gazelle]

Anyone can help me in dm? Because i cant send images here, i need a book that shows a specific kind of math questions

[versed charm]

Hello, can anyone recommend me a book wich it starts easy abt geo olympiad problem strategies? I struggle a lot with this type of problems and i would like to read something that includes some tricks to start with it (srry for the horrible english, im spanish btw)

[still panther]

I guess we can just go to the complete metric on the perfect set and conclude that it cant be countable because baire, yeah thats pretty easy ok

[remote vortex]

Indeed

Big hint: ||If X is perfect, then the complement of every singleton is a dense subset of X||

[remote vortex]

Wait, a perfect set is by definition closed

And a closed subset of a complete metric space is itself complete (with the same metric)

[still panther]

indeed

[remote vortex]

So yeah, my suggestion works

[maiden glen]

what is a book I may read to effectively learn how to read and write in japanese writing system and its syllabaries?

[graceful moon]

I was going to say this isn’t really the best place for this but given the number of weebs.. yeah fair enough

[maiden glen]

i study languages and mathematics and according to the description of this channel 'feel free to ask about any other literature' this may not be a conventional request, but it is still acceptable.

[maiden glen]

also you should get used to the fact that not everyone who wants to learn Japanese watches anime, I for instance; do not like it.

[graceful moon]

https://www.merriam-webster.com/dictionary/joke

[jaunty quail]

Whats the new hot topic?

[hallow oriole]

alg geo ofc

[heady ember]

I only ask after sufficient time has passed thinking about it. In general, I try to do things by myself, as much as possible.

[heady ember]

lmfao

[misty galleon]

Does anyone know of any quality calculus-based introductory physics textbook? I'd like lots of exercies, good explanations, and atleast odd number answers

[viscid oasis]

does anyone have an introductory book to differential geometry?

[dim sierra]

Differential Geometry of Curves and Surfaces by Tapp

You could also look at Shifrin’s or O’Neils’s book

Whatever you do tho, don’t use doCarmo

[dapper root]

Real

[sage python]

For curves/surfaces I thought Do Carmo was better than Shifrin based on friends of mine who looked at them

[remote sparrow]

i thought shifrin's "book" was just a compilation of lecture notes?

[dim sierra]

Yeah it is

I think the exercises are good though

[lime vessel]

Jeffrey M. Lee

[graceful moon]

Kobyashis curves and surfaces book is great because it actually uses differential forms and all that

So it’s basically all that a diffgeo course would be just without you needing to know about topology and manifolds

[abstract copper]

How much topology do you really need to know for Lee's smooth manifolds?

[graceful moon]

Not much, can also just jump straight in there

I wish I could share my course notes for the geometry class I took though, I legitimately think they’re better than any curves and surfaces book I’ve seen

They’re based on Kobyashis book but I think far superior

[abstract copper]

I want to study topology as well as diff geo but TIMEEEEEEEEE, and the courses I will be taking doesn't really require topology 😦

[graceful moon]

Like I know it doesn’t mean much because no one can actually use them, but my the notes my course used took a very differential forms first and I think it lead to an actually good curves and surfaces course

You get to do all the fun stuff without getting bogged down with charts, vector bundles or anything like that which I think is great for a first course

[reef escarp]

whats the "basic mathematics" by serge lang of physics? (high school physics covered in a concise and nice way)

[native cradle]

is The USSR Olympiad Problem Book good for recreational maths?