book-recommendations

[rare estuary]

I have both so I guess I will see if one speaks to me more. Do you think Understanding Analysis/Spivak is enough background for Browder?

[sage python]

You should be good if you also know some linear algebra

[rare estuary]

Cool.

[misty wyvern]

What is the worst, most error-prone math textbook out there

For reference, Janusz is cited in multiple places as being the worst calculus textbook but I'm aiming a bit higher, maybe graduate-level textbooks that everyone hates.

[crimson leaf]

While a lot of people use it Royden has an errata of about 13 pages

Introduction to smooth manifolds by Lee does as well but that book is longer iirc

[remote sparrow]

Model Theory by david marker is a standard graduate text that's known for having a long errata webpage

i wouldn't know about it being one of the worst

[sage python]

Weibel is a pain

[molten temple]

iirc hubbard vector calc book had a pretty long errata

[median panther]

Warrior Cats

[rich prairie]

I'm currently reading this. https://en.wikipedia.org/wiki/A_History_of_Vector_Analysis

[narrow relic]

Do you have a source for problems to do from that book (Kolmogorov and Fomin, Introductory Real Analysis)?

[sage python]

Sadly no. Part of my analysis class used it but it was a different translation titled "Elements of The Theory of Functions and Functional Analysis"

And the prof just wrote his own problems

[heady ember]

Look in pinned

Personally I'm using Jacobson's Basic Algebra I, its been great so far. But I'll probably get slapped increasingly hard soon

On a side note, its so weird to see sloth as grey lol

[finite gale]

Is a gray not a sloth color

[heady ember]

Its just that I've gotten quite used to sloth being blue/pink lol

[tough moon]

Best books to learn and understand Linear Algebra and Multi variable calculus

[narrow relic]

Okay. Thanks anyway 🙂

Isn't that book extremely terse?

[sage python]

Probably on the terse end given that it was inspired by Rudin

Honestly I don't dislike Rudin lol

[narrow relic]

Got it.
Do you have an opinion on Carothers by the way? I spent a decent amount of time on it in 2023 but got kind of burned out

[sage python]

Glanced at it once way back in the day, seemed decent enough. If you've already started then maybe that's not a bad idea to see it through

Already used to the expo style and whatnot

[narrow relic]

I might pick it back up. I appreciate the advice.
I find the writing style somewhat sloppy and annoying but I end up thinking that about almost every math book I read

[narrow relic]

I actually picked it up for a weird reason: I was looking for a book that had a kind of slick type of notation that I saw a professor using, and it was the only book I could find on analysis at my level that looked like the kind of notation he was using.

[sage python]

Ah, if you didn't particularly like it then don't bother. I was thinking if you already had some momentum or smth

[narrow relic]

I spent 5 months on it or so, working about 1 hour a day, I think

Which is a pretty large amount of momentum for me

I have probably over 100 pages of notes on it in a large font

And I did all of the triangle-marked problems up until where I stopped

[sage python]

Yeah I guess it depends on you then

Tbh I went off classes more than books, and referenced different books for different parts of the class

[narrow relic]

I think that's probably the best way to go, from my experience now

[sage python]

My first analysis class used a mix of Rudin and "Fundamentals of Mathematical Analysis" by Sally

Rudin was where I learned most of my metric topology and it was p nice for that. Sally... I think if we had stuck to it and worked linearly it would've made more sense

But we didn't so some stuff was odd. Also it's a quasi-IBL style book

Toward the end we used Buck Advanced Calculus which is dogshit

[narrow relic]

That's funny, I always see older professors recommending that book

[sage python]

Occasionally for multi stuff I tried to reference Spivak Calc on Manifolds or Munkres Analysis on Manifolds a bit but they were a bit different than Sally and in any event that whole part of the class was a mess. And I think the curves/surfaces bit (where we used Buck) I just gave up on trying to figure out lol

[narrow relic]

I try to reference the Spivak one too but it ends up not working

There's a book by Fleming for the multivariable stuff that might be good but I have never had time to read it closely

[finite gale]

I thought they stopped using Sally after he died

[sage python]

Soug rediscovered it for a while

Unfortunately

I mean idk maybe if we just stuck to it it would've been fine

[narrow relic]

I appreciate you sharing your experiences

[sage python]

But Soug doesn't work well dual wielding books

He kinda does one chapter here one there

And then there's a mismatch

We also had to teach ourselves linear algebra from Hoffman-Kunze

[finite gale]

Neves just used royden after running down ladw for 4 weeks

[sage python]

Which didn't get to inner products until quite late in the book. So Sally, which did LA in an appendix

Was willing to use Riesz rep implicitly during the multi bit

To talk about gradients

But we didn't know Riesz rep since we used HK rather than Sally

[finite gale]

We never did arzela ascoli or omt or the other big one

[sage python]

So when Sally is saying gradient f(x) . h

We're all like

What is this yappanese

Dot product of a linear map with a vector?

[crimson leaf]

So what exactly is the point of a book like Carothers compared to just picking up a measure theory book?

[sage python]

So yeah the mismatch with book juggling coupled with Soug being Soug made that whole class a bit of a shitshow

[sage python]

I've heard this is good. Does measure theory for multidimensional integration

Which is good because Riemann integral doesn't work nicely after 1-D

[finite gale]

What was the worst (math) class you took in undergrad

[sage python]

As anyone who tried to glance at Munkres Analysis on Manifolds can tell you

[sage python]

Hmm... The one I learned the least from was second quarter grad algebra. Prof couldn't decide if he wanted to teach a commalg course, varieties course, or schemes and cohomology course

So the answer was: yes

[finite gale]

Oh

That class is in good hands now

[sage python]

So it seems

Also since this is now about classes more than books I'll move

[remote sparrow]

you can skip the measure theory material in carothers if you want. but it's a good source to go after single-variable analysis from a book like abbott.

basically a pretty leisurely and detailed treatment of metric spaces and function spaces

it would segway nicely into folland

you can read less general treatments of measure theory instead of folland if you want though

[sleek ice]

Any decent self study galois theory books?

[finite gale]

Rotman has a section on it I think

Rotman good

[remote sparrow]

https://www.amazon.com/Galois-Theory-David-Cox/dp/1118072057

[sleek ice]

Damn, these book costs will make me poor

[tough moon]

Best books to learn and understand Linear Algebra and Multi variable calculus?

[trim kayak]

Any recommendations for interesting math books that aren't too advanced?

[finite gale]

what is "too advanced" here

and what are you interested in learning

[trim kayak]

I'm interested in learning about theories, anything relating to algebra, geometry, and stats. I got a recommendation last night from somebody here. The first half is good but the last half is very advanced and too in depth

[crimson leaf]

What is your background

[trim kayak]

I have a BS and MA degree but not in math. I'm currently a Special Education math teacher at the high school level. I don't teach higher level courses but I really like math and want to read more about it

[crimson leaf]

Are you looking to learn university level math or?

[trim kayak]

Yeah I suppose. High school and university level

[crimson leaf]

You should probably learn proofs if you haven't already . Personally I like book of proof my hammock

[trim kayak]

Oh proofs. I'll look into that one, thanks. Any others?

[trim kayak]

I found an online pdf of Book of Proof. I scrolled through it and it looks advanced! I'll try reading through it

[crimson leaf]

Yeah it's free online by the author

[trim kayak]

Looks like a hard one to read. I'll check it out

[gray gazelle]

Hello guys. I am doing self-study of 5 subjects.
Real analysis, proof writing, abstract algebra, number theory and linear algebra.
I am using
Abbott's book for real analysis
Farleigh's for abstract algebra
Velleman for proofs
Friedberg for linear algebra
James strayer for number theory.

Is this combination fine?

[remote sparrow]

yeah

[heady ember]

Doing all 5 at once may be a bad idea though

[crimson leaf]

Especially if you're taking classes

[molten mason]

Read Chapter 1 of all 5 books, then Chapter 2 of all 5 books, then Chapter 3 of all 5 books...

[molten mason]

They're fine, but go through the proofs book first. Chapter 7 will set you up to go right into the number theory book.

You'll need a good proofs understanding before you get into real analysis, Abstract, and Friedberg's Linear Algebra

[heady ember]

Vellemen might not be necessary, you can feasibly hop straight into something like FIS or Abbott if you wanted to

[smoky zephyr]

me reading all of book of proof and still not being able to do abbott

[sudden kindle]

What are you struggling with,?

[crimson leaf]

Honestly something like Lay might be good for this scenario since he starts with proofs. I honestly didn't think I would like this book but it's not bad

[molten mason]

Perhaps, I personally learn from reading more and more proofs in various texts, but if they just read it without spending too much time on exercises it can be a quick read, such as this weekend.

[gray gazelle]

I have some experience with some. Like I have already done the first four chapters of Gallian. For proof writing, I have studied the book "how to think like a Mathematician". And some experience with linear algebra from Howard Anton book

[trim kayak]

Is Friedberg's Linear Algebra pretty good? I'm interested in reading various books relating to Algebra, Geometry, and Stats. I just don't want anything too dry or advanced.

[gray gazelle]

Oh yeah. But unfortunately, we don't have any faculty of professors for pure mathematics.

[gray gazelle]

I have studied the book "how to think like a Mathematician". And currently on 3rd chapter of velleman's book.

[gray gazelle]

I have made a schedule. One day I study real analysis, number theory and proof writing. Then, the next day abstract algebra, linear algebra and proof writing. And repeat this cycle.

[heady ember]

Why do you need to use Velleman if you're doing that

[gray gazelle]

Maybe. But velleman's book had helped me a lot.

[heady ember]

And doing 6 books concurrently is a bad idea, probably

[trim kayak]

I want to study some of these but I think they may be too hard 😢

[gray gazelle]

Actually 5. (I have already read the book : how to think like a Mathematician).
But yes you're correct. I can't manage 5 books, but I try to more focus on real analysis, abstract algebra and proof writing

[heady ember]

Why not just do 2-3 at a time

I don't see the reason for your insistance on doing 5 books at a time

[gray gazelle]

Oh wao. How do you manage to do those problems that you can't solve? Like today, I was reading abbott (limi of a sequence). I saw some exercises, some were easy. But some exercises doesn't make any scene to me. I give up so quickly (on some). Then I peek at solution manual.

[heady ember]

If you only do those exercises that are easy you won't learn as much

[gray gazelle]

But I am trying to do most exercises by own, but sometimes my own proofs and solutions doesn't looks me correct however I can't find any mistake too.

[heady ember]

If they don't look correct you should find out why.

You shouldn't just leave it hanging

[gray gazelle]

I used all 5 because I thought all subjects have some relation with each other. Like number theory is used in abstract algebra Moreover linear algebra too.

[gray gazelle]

True.

[trim kayak]

Are you taking college level classes, Grothendieckfan?

[heady ember]

I don't see why you can't, for example, learn anal + lin alg first. Then do alg + another book.

Good books will motivate the theory with links to other fields, where relavant.

[molten mason]

Just keep at it.

[gray gazelle]

For example: the first exercise in Abbott 's 2nd chapter is :
" .. def : a sequence (xₙ) is verconges to x if ∃ ε>0 s.t for all N ∈ ℕ it is true that n ≥ N implies |x ₙ -x|<ε... What exactly is being described in this strange definition ".

Here my answer was : in the definition it is described that there is a fix ε s.t for every natural number N, any natural number n s.t n≥N satisfies |x_n − x|<ε. Then the sequence is verconges to x.

But in the solution manual aithor write the definition says any bounded sequence is vercongent

[molten mason]

Yes. It's the textbook my university uses, so I have no choice

But it's a good book and recommended often by a variety of people in this channel.

It's just more proof heavy, so it can considered dry if that's not what you're into. There's other books that are more like, problem calculation nooks that non-pure math majors would use

[heady ember]

Are you sure he says any bounded sequence is convergent

[gray gazelle]

Not convergent, its vercongent.

[heady ember]

[gray gazelle]

Lemme send screenshots

[heady ember]

Eh sure, never heard of that term before

[gray gazelle]

I can't send pic in this discord?

[heady ember]

Oh you don't have pic perms then

[gray gazelle]

Oh

[gray gazelle]

Oh. In the hope that you shall try again in future?

[gray gazelle]

Can I send you in dm?

[heady ember]

Sorry, I don't accept dms from people I don't know.

[gray gazelle]

Ok. No problem

[heady ember]

Ah ok found it

[gray gazelle]

Yes this one.

[heady ember]

Yeah what about it though

I misread what you sent just now. Now that I look at this, yeah it makes sense that such a sequence is bounded.

[gray gazelle]

Yes. But when I was answering the question. My answer was totally change.

[heady ember]

What?

"totally change"?

[gray gazelle]

And I was in doubt, that whether I am giving the correct answer or not. So I quickly look into solution but my answer was incorrect.

[heady ember]

You are actually just quoting the definition here

The author wants more depth and insight than that

[gray gazelle]

Author says : the definition says every bounded sequence is vercongent

My answer was : the definition says we have a fix number ε so that every natural N, if a natural number n≥N then |x_n −x|< ε.

[gray gazelle]

Sadly, but yes.

That time, I didn't understand what to do other than quoting.

[gray gazelle]

Oh

[heady ember]

Yeah its natural when you're starting out. But if it's clear to you that you're not fulfilling the exercise's demands you shouldn't just look at the answer imo.

If you're not sure what the exercise wants, you can ask in this server, for example.

I don't look at solutions. Rather, it's probably better for your learning to look for hints. My personal guideline is that I won't ask for hints not at least untill I exhaust all my ideas, and at least spent a couple of hours thinking about that exercise.

A nice paragraph about the importance of challenging yourself in math.

[young grove]

chaos theory and fractals my work usually includes creating visual graphics. so knowing about these might help. any book recommendations for these

for fractals I think complex analysis are what I need to look into

[dusk wind]

@trim kayak is there a particular algebra you want to learn?

theory can often be very dry+advanced but there may be certain subjects you find of interest

[trim kayak]

I'm not really sure actually. I took various algebra classes in high school and college. Maybe something slightly more advanced, such as theory. I want something to keep my interest and to avoid things that are dry and hard to understand.

[dusk wind]

you're gonna need to accept some of those dry and alien concepts then

there's a reason why stuff like that isn't taught at that level

I wouldn't recommend this but for your case it's probably useful https://venhance.github.io/napkin/Napkin.pdf

[trim kayak]

That makes sense. I enjoy algebra and practicing problems every once in awhile. Seems like I should move ahead into something like theory but I'm not sure if that's best. I'll look around for things to read/learn

Thanks

[dusk wind]

number theory is good, stats is very useful and not too abstract

you might get motivated to branch out into more abstract stuff from the more practical forms

[trim kayak]

I love stats. Took a few basic stats classes. Maybe I'll look into more advanced stats. That napkin pdf looks tough!

[dusk wind]

its mostly good to introduce those concepts so you have options of what to study in a better more specialized book

high school teaches with theory removed, so try more theory or a different approach

[trim kayak]

Have you read through the whole Napkin pdf? It's a long one too!

[dusk wind]

nope

more stats https://stat110.net/

[trim kayak]

I'm going to look through that pdf. Any others you could recommend? Are you studying math at all?

[dusk wind]

just a bunch of diiff subjects

[trim kayak]

Very cool.

[dusk wind]

but any book is good in general so just read anything others recommend

[trim kayak]

Are you a student?

[dusk wind]

sure

[trim kayak]

Nice

Sounds like you're studying different subjects but wasn't sure if you're taking classes for a degree or anything

[dusk wind]

complex motives, off topic

[trim kayak]

ahh

Do you read novels too or mostly academic material?

[dusk wind]

books on math but mostly interested in their history, also with how classical authors wrote you could count those as novels too

[trim kayak]

Ahh okay. What's your favorite book that you've read about math?

[dusk wind]

too many, anything that is neutral and to the point probably

this book for example is interesting https://amazon.com/Concrete-Approach-Abstract-Algebra-Mathematics/dp/0486824616
it teaches concepts you already know from algebra but presents them in a very light manner

[trim kayak]

Oooh that one looks good. I'll have to check this one out too

Thanks!

[gray gazelle]

I am sorry for the late reply (I had an appointment with the doctor that's why I didn't reply).

Oh I understood it.
One more thing. Suppose you have proved some exercises problem. (The book doesn't contain solutions) how you will verify your proof?

Many times I come up with my own proof, and I feel confident about it. But when I look at the solution, I find the author had written the proof in more rigours manners (giving more details and insight).

Sometimes I have some questions, but I have no one who can answer (before this server). Then I gave answer by myself. For example : In Abbott's book theorem 2.2.7 is to prove if limit of a sequence exists its unique (proof is left). My approach was :

Suppose (x_n) be convergent sequence. Let (x_n)→a and (x_n)→b. Suppose ε >0 be arbitrary. Choose N_1,N_2 ∈ N s.t • •• (some steps) •• • |a − b| < ε. Therefore a=b.

Here I have chosen two different N's (N ₁ and N ₂), because if sequence converges to "a" then there must b some N also since sequence converges to "b" so again there must be N , but it isn't necessary that both will be equal so I took two different N's.

But why we are not taking two different ε?
(My ans : because ε is arbitrary, (it is not a fixed number) so we assume the ε is same for both limit points. However taking two ε's doesn't harm the proof, but doing this we have to pick minimum one, [ is it correct answer]).

[gray gazelle]

This is really impressive. Words of reality. Thank you bro.
(Can I know the name of the book, from which you took a screenshot?)

[heady ember]

Author: Bernd S.W. Schroder
Mathematical Analysis: A Concise Introduction

[heady ember]

how you will verify your proof?

1. Read it step by step to yourself, carefully filling in any and all gaps you reasonably left to the reader, and see if you find any logical fallacies. This is what I used to do.
2. Ask people here to help you check your proofs.
   It takes time and experience (and also feedback) to get better at proofs.

My approach was: ...
This is not exactly the way you write a mathematical proof. After stating the proof you have, you can just exit the room (of course, leaving the latter 2 paras may serve well as a knowledge check)

That is, only this part is necessary before you can \qed

Suppose (x_n) be convergent sequence. Let (x_n)→a and (x_n)→b. Suppose ε >0 be arbitrary. Choose N_1,N_2 ∈ N s.t • •• (some steps) •• • |a − b| < ε. Therefore a=b.

Also, instead of saying "Suppose ε >0 be arbitrary" which is unnecessarily long, consider simply stating "Let e>0". Also, "Choose N_1,N_2 ∈ N" sounds like you're making an arbitrary choice that satifies "..." criterion. Whilst a reader familiar with the material would know you mean to imply the existance of such N's, a good mathematical proof would perhaps opt to use phrases such as "there exists". Lastly, it is reasonable to say "There exist N such that ..." instead of explicitly stating N_1 and N_2. You can expect the reader to know you mean to take N:=max{N_1,N_2}.

[glossy zealot]

I have good experience with asking people in this discord to verify my proof

And I learned a lot from it

[gray gazelle]

I got it.
So I should be clear at every step.

Proof : Suppose a sequence (x_n) and, (x_n) → a and (x_n) → b. Let ε>0. There exists two natural numbers N_1 and N_2 that satisfies
n≥N₁ implies |x_n −a| < ε/2, and
n ≥ N₂ implies |x_n − b| < ε/2.
Set N:= max{N_1,N_2}. Then, for n ≥ N consider
|a − b| = |a − x_n +x_n − b|
≤ |a − x_n| + |x ₙ −b| < ε/2 +ε/2 = ε.
Therefore, a = b.

[gray gazelle]

Wao. I shall try too.

[gray gazelle]

From the entire conversation I learned :
(1) Instead of studying from 5 book I should use 2 − 3.
[ I shall use 3, real analysis, linear algebra and proof writing]

(2) I shouldn't skip hard problems, instead of this I must spend a reasonable amount of time (like about 2 hours per day).

(3) The initial goal should be to prove/sol the statement by itself. But if all thoughts and ideas do not work. Then I should seek a hint (not solution).

(4) Do more exercises specifically proof base.

(5) The goal is to seek insight of the exercise problem, instead of only throwing solution.

(6) The proofs should be neat and clean.

[gray gazelle]

Could you please tell me where I should ask for checking my proof?

[glossy zealot]

There is a channel in this discord called real-complex-analysis

You can post your proofs there and ask for help

[gray gazelle]

Understood. Thank you man.

[glossy zealot]

I tagged you in a message in the channel

There are a lot of wise people there, ranging from super smart undergrad, graduate students, and even experienced professors

[gray gazelle]

Quantum Mechanics by F. Mandl is a great book because one can read it by focusing on the equations. The idea is that eventually one gets used to them, and things start making sense. There is no heavy monologue, "exercises", irrelevant / out of context parts, to distract the flow of my formal thought. I enjoy this book very much.

If you believe you have come across texts (especially about category theory, representation theory, QM / QFM) which / that you think are "similar" please tell me.

[gray gazelle]

Omg wao. I hope I will learn from them. And I will learn as much I can.

[heady ember]

I would probably write something like this:
\begin{proof}
Let ({x_n}_{n=1}^{\infty}) be a sequence converging to both (a) and (b), and (\varepsilon>0). By definition, there exists (N \in \mathbb{N}), so for all (n \geq N), we have (\lvert x_n-a \rvert < \varepsilon/2) and (\lvert x_n-b \rvert < \varepsilon/2). Then,
[\lvert a-b \rvert \leq \lvert x_n-a \rvert + \lvert x_n-b \rvert < \varepsilon/2 + \varepsilon/2=\varepsilon.]
Thus, (a=b).
\end{proof}

In many aspects of proof-writing, there often isn't a hard and fast rule so don't take it as that. For instance, some would prefer to omit "by definition" for conciseness.

oops i forgot to add a line

[gray gazelle]

Wao. This is so concise. But can I ask, why you took same N for both? However, it isn't necessary that both sequences fall into ε neighborhood after same point.

[heady ember]

Lastly, it is reasonable to say "There exist N such that ..." instead of explicitly stating N_1 and N_2. You can expect the reader to know you mean to take N:=max{N_1,N_2}.

[gray gazelle]

Ah I understood. Btw was my proof incorrect?

[ sorry, English is not my native language so I make many mistakes]

[hasty eagle]

grass

[heady ember]

Looks fine in terms of rigor

[gray gazelle]

So I can reduce this too.

[heady ember]

wdym "this"

[gray gazelle]

Still need improvement right?

[gray gazelle]

I mean the sentence " There exists N_1 and N_2..."

[heady ember]

Yeah seems about right, but I'm just gonna add a couple things.

1. "reasonable amount of time" keyword is reasonable, don't overdo it like I did last time, lest you find yourself unnecessarily exhausted from, say, trying to prove each and every detail by youself.
2. "(4) Do more exercises specifically proof base." depends on the goal of your learning. If you want to get into engineering, for example, perhaps proof-based mathematics is relatively unimportant

[heady ember]

In terms of phrasing, it can be improved.

[heady ember]

Yeah no need to write that, you can just have a single N and its generally understood

[gray gazelle]

Noted.

[heady ember]

Also this is #book-recommendations so reply me in another place if you wanna continue the convo. Say, #math-discussion. Has been getting offtopic for far too long oops. But I gtg anyways bye

[gray gazelle]

Yes. Your right. Bye and thank you

[heady ember]

np

[strange vector]

does anyone know the level of Foundations of Mathematical Logic by Haskell B. Curry? Is it too hard to read for first course for logic

[smoky zephyr]

i tried chapter 2 like 2 years ago and everything was too hard so i just gave up

[sudden kindle]

Try again

Sometimes when you return to things after some time it turns out that you can do it

[tough moon]

Books to best learn and understand Linear Algebra and differentiational equations?

[trim kayak]

This book was recommended to me by somebody in here https://home.cs.colorado.edu/~alko5368/lecturesCSCI2820/mathbook.pdf

Haven't started reading it yet. Looks interesting but hard 😦

[tough moon]

Gonna use it, thx

[remote sparrow]

that's not a link to more stats, it's probability

[remote sparrow]

https://maa.org/press/maa-reviews/foundations-of-mathematical-logic

i wouldn't know about it being "too hard" but it seems unsuitable regardless

[strange vector]

thank you

[rapid lily]

We used this book for my differential equations course: https://www.jirka.org/diffyqs/diffyqs.pdf

Also for linear algebra, Shaum’s linear algebra and applications is like the other book musicmeg23 recommended. There is also linear algebra by Hoffman and Kunze which is more theoretical

[remote sparrow]

#book-recommendations message

#book-recommendations message

[trim kayak]

Any book recommendations for data science? I want to read and learn more about it

[opaque ruin]

Can u recommend me hard problemset for Linear algebra and probability for Olympiad's and master participating?

[rapid lily]

I got a book recently the video I watched said it is like a standard text for statisticians and data science. “Statistical Inference” by Casella and Berger

[trim kayak]

Ooohh thanks

It looks like a hard one to get through but I will check it out

I think I'm looking for basic stats books. I know some stats, but some books, like the one you shared, look very advanced and may be hard to understand. I don't want anything dry either because I'll be less interested in reading it

[rapid lily]

Yeah I think that one is like for grad school, and professional level, so if you went into the field that would be a good one to have as reference. I think they said first two chapters is good for applications in other fields

[trim kayak]

It looks like a good one though. Do you know of any that are slightly more basic than that? So many people here talk about upper level/grad level math and it's way above my knowledge

[gray gazelle]

beginner friendly integrals/derivatives? preferably cheaper than 30 euro, if anyones from greece then that could help too

[dusk wind]

what else besides algebra and calculus is taught in high school

application is just watered down theory

[trim kayak]

Geometry, Stats, Trig

[tough moon]

☑️

[dusk wind]

anything that isnt geometry is hard then in that case

[trim kayak]

Kind of, yeah. Solving an equation in algebra isn't too bad

[dusk wind]

but theres diff algebras

[delicate mango]

hey can some of you can recommend any mathbook that is written with passion?

[trim kayak]

True. I really like the basic stuff. Have to get into more advanced algebra topics sometime

[dusk wind]

I wouldn't say they are advanced, just different

[trim kayak]

mhmm

[remote sparrow]

can you elaborate on what "basic stats" is to you? also, you want to be careful not to conflate probability with stats

what do you mean by knowing "some stats?"

[trim kayak]

I took a few stats classes in college that seemed basic. Learned about standard deviation, some quantitative and qualitative analysis, the normal curve, statistical inference, various tests such as ANOVA and t-test, and even some probability. To me, that seems basic. I want to learn more about that for now and then maybe move to more advanced topics. I really enjoyed the basic stuff 🙂

[dusk wind]

I would hope that the typical college course has that

there's probability in stats so it doesn't really matter

however probability theory is important, so good material on it is still worthwhile

[trim kayak]

Yeah. That's the stats I'm familiar with. I really enjoyed it

ahh okay. Ill look into theory too

[dusk wind]

also college courses like to blaze through content so sometimes there can be gaps/necessary refreshers

[molten mason]

Prob/Stats for Math majors and non-Math majors are sooooo completely different, at least locally for me. Two separate worlds.

[trim kayak]

Makes sense. I just really enjoyed the basic stuff if that's what basic stats is. I don't know

Any recommendations for basic stats books, Salagos?

[molten mason]

Nope, sorry. Unless someone else here has a concrete answer, I would say best bet is to search various forums and reddit. You're normally not just using stats for the sake of it, you're going to be using it specifically for something, so I'm sure you could google "statistics for XYZ" such as engineering, biology, psychology, etc. Just googling "statistics books for beginners reddit" popped up a bunch of things.

[slender cargo]

My understanding is that if you want to learn stats at an advanced level, you need to learn Measure Theory

[molten mason]

The big thing is why do you want to know more about it. What is your purpose and end goal. That will guide you down a better pathway.

[dusk wind]

the why is more important than the book

[trim kayak]

Thanks guys. I really enjoyed Stats and have some background in research. I don't want to get another degree but want to keep reading/learning about what I've learned. I should go beyond it but really liked the basic concepts of stats

[dusk wind]

but if you took it in college then you already have practical knowledge of it

any more advanced than that and you might as well get another degree in it if possible, math is worth pursuing for its own sake

[trim kayak]

Yeah but I can read various books and things that's more advanced and not have to get another degree

I'm calling the previous concepts mentioned as basic. What's a step farther than that, theory? Or Measure Theory as TopDreg mentioned?

[dusk wind]

its very difficult to be self taught in those subjects, it can get boring and such very fast

also... many books do not have answer keys

[trim kayak]

I'm calling the previous concepts mentioned as basic. What's a step farther than that, theory? Or Measure Theory as TopDreg mentioned?

Good point

[dusk wind]

what is your motivation for these subjects if not as a student?

[grave vapor]

Algebra to Calculus by Mike Goldsmith is a fun and interesting read

[slender cargo]

Speaking as someone who is going to be a student again, it's fun to learn this stuff for its own sake

I don't think we need to question their motivations

[dusk wind]

if you just want to know of books on every subject you could just visit https://realnotcomplex.com

[dusk wind]

they've inquired on multiple books on multiple subjects

[molten mason]

100%, you can just do it self-taught. What Renji means is just how much can be required.

For example at my university, before you can even take the first statistics class, it's required to take a semester each in Probability, Calc III, and Proofs.

If you want to learn more about theory, it's going to require a stong math background.

If you want to learn more about application in a certain field such as for work, each field has its own textbook specific to that field at various levels.

[trim kayak]

Just because I like math and want to read/learn more about it

[molten mason]

For example there is Introduction to Mathematical Statistics by Hogg, Mckean, and Craig

[grave vapor]

also the illustrated history of mathematics has this massive poster thats a historical timeline of mathematics, figures, discoveries, other historical events that happened alongside the discoveries

[rare estuary]

I like this book

[grave vapor]

Adding that to my wishlist

[dusk wind]

definitely visit the site I linked for an organized list of recommendations on books most will probably mention here

[trim kayak]

I will do that. I just bookmarked it. Thx.

[molten mason]

Introduction to Mathematical Statistics by Hogg, Mckean, and Craig
Weighing the Odds: A Course in Probability and Statistics by Williams
Statistics for Mathematicians: A Rigorous First Course by Panaretos

[dusk wind]

Just pick a book or two for your learning path

[trim kayak]

That looks like a good one. I just found the pdf. Looks hard but interesting

[trim kayak]

Thanks

[molten mason]

Yeah we're not trying to discourage you with 100 questions, but there's 100 books out there and we need to know your level of math, your goal, etc to figure out the best one for you.

Hopefully those 3 are a good starting point, the first and third one are more math heavy. The second one might be the most appropriate, but take a look at each one and skim through them and make your own decision and go from there.

No problem, good luck!

[trim kayak]

I prefer hard copies but have so many books already. PDFs can be nice too. Are you studying math as a student?

[lilac raven]

any good recommendations for an intro book on operator algebra/banach algebra?

[molten mason]

The majority of the people in this server are, including me. This place is full of everyone from high school students to university professors. There's tons of researchers and applied people in here too though.

[slender cargo]

Just to add on to what I mentioned earlier, if you look into how Probability Theory is done, then Measure Theory is generally mentioned as being important. And to get to Measure Theory is its own journey (Measure Theory will usually be part of a graduate Real Analysis course for a Math PhD candidate). So maybe look into that as a possible path?

Perhaps Stats PhD candidates go about a different path though.

I say this as someone who has yet to learn Measure Theory. From what I've seen about Probability Theory, Measure Theory gets listed as being very important.

[trim kayak]

That's good to know, thanks. I have quite a few recommendations now. Have to look at those and decide which one to start with. Or maybe read a few at the same time

This may be a dumb question and is subjective, but how do all of you read through math books? Do you read a chapter or two at a time every day? Do you read a chapter or two, practice and apply what you've learned, and then move on? I'm guessing it's best to read daily?

[gray gazelle]

I dont mind if its in greek nor english id love id anyone could help me find a beginner calc for dummies book thats relatively cheap lol

[remote sparrow]

did your classes involve calculus

[trim kayak]

I took a few calculus classes when I was studying pre-pharmacy. Now that's one branch of math that I just don't understand. I studied like crazy and passed the class, but still just don't understand it at all

[trim kayak]

https://www.amazon.com/Calculus-Dummies-Math-Science/dp/1119293499

[remote sparrow]

you don't understand calculus or you don't understand calculus-based stats?

[trim kayak]

I don't understand calc

[remote sparrow]

you should refresh your knowledge of calculus

or perhaps learn it again with some fresh eyes

https://stat110.net

https://www.amazon.com/Mathematical-Statistics-Applications-Dennis-Wackerly/dp/0495110817

these books assume you have calculus background

[trim kayak]

Oh okay, thanks. I'm sure it's easier for others, but it was a hard one for me.

This may be a dumb question and is subjective, but how do all of you read through math books? Do you read a chapter or two at a time every day? Do you read a chapter or two, practice and apply what you've learned, and then move on? I'm guessing it's best to read daily?

[dusk wind]

100 pages a day

[trim kayak]

That's a good idea. Do you do that?

[dusk wind]

if its good yea

how else are you going to finish reading it?

[remote sparrow]

you should read with a pencil and paper in hand

[smoky zephyr]

can you not troll when people are asking genuine questions

[dusk wind]

I'm being serious

[remote sparrow]

feel free to try some of the examples or fill in gaps between steps

[trim kayak]

That was my next question. Would you suggest taking notes even if it's learning just for fun by myself

[remote sparrow]

i don't take notes personally. but a lot of people do and it works for them

taking/not taking notes is not a matter of "intelligence"

[dusk wind]

if you take notes that will make it take longer but you can do shorthand

[remote sparrow]

just want you to know

[dusk wind]

there are definitely 'intelligent' notes though

[remote sparrow]

taking notes is just simple, actionable advice

i shouldn't be perceived as "smart" for not taking notes

[molten mason]

It depends on the book... some can easily be a chapter or two a day. Some can take an entire day to do a couple of pages.

Set yourself a goal such as an hour a day or whenever your brain is fried. Split it into two, morning and evening.

[dusk wind]

don't smart people take notes though

[cedar ridge]

Why you always in this channel @remote sparrow 💀

[remote sparrow]

i like this channel

[trim kayak]

Makes sense. Sour is very helpful

[dusk wind]

showing up to class is smart actually

[molten mason]

I have notebooks FULL of notes that I have never looked at after writing them down lmao

[remote sparrow]

for some people, taking notes is a way to actively engage with the material

[dusk wind]

better idea, put your feet up on the desk and don't take any notes, get an A

[remote sparrow]

notes are not necessarily for reviewing

[molten mason]

In fact I'm filling out one right now, that I will probably never look at again.

[molten mason]

This

[remote sparrow]

some people just prefer to listen in lectures

[molten mason]

It keeps my brain from wandering. Or it helps me visualize something.

[dusk wind]

yea if you don't take notes you'll start to daydream about that thing you didn't do

[molten mason]

I'll never forget this one girl who never ever brought a pen, paper, or even a backpack to class. Sat in middle of class. Stayed quiet and listened. Got an A on her exams.

[dusk wind]

If your teacher is really good the lecture should be your notes

[molten mason]

I've been taught and under the assumption that your textbook should be read before class, so when you show up to lecture it's just to review and solidfy the material and answer any questions.

[trim kayak]

I agree. I always took notes in college. Helps me remember what was talked about during class and important points to study from for a test or quiz. All of my classes were too much information not to take any notes

[manic cairn]

i have never successfully taken notes on most things.

in math, if i don’t remember i just use a reference and do problems until it’s memorized

or use a reference

whereas for literature i have no idea what constitutes “noteworthy”

[trim kayak]

That makes sense too. I agree. What are important notes for literature. Good point.

[manic cairn]

this probably isn’t something you should emulate

[trim kayak]

I'm just making a statement and saying I agree?

[manic cairn]

i’m not saying that a noteworthy part does not exist or that notes aren’t worthwhile. i’m saying i’m impaired and have poor skill

with regard to notes

[gray gazelle]

I’m in British sixth form studying maths and further maths a level and I’d like a book that will basically cover all of calculus from my level and beyond.

Anyone know of any

[snow valley]

Is the book of proof good for beginners

[remote sparrow]

yes

[lime sapphire]

honestly I'd advise sticking to A level books until after you've covered your syllabus to learn any calculus material that's more advanced

regardless here are a few suggestions

https://archive.org/details/piskunov-differential-and-integral-calculus-volume-1-mir

and
https://archive.org/details/piskunov-differential-and-integral-calculus-volume-2-mir

are freely available volumes of books by piskunov and they're pretty friendly while also teaching you everything you need

spivak's calculus, for an A level student, is useless unless you're some genius and won't knock yourself unconscious by smacking your head against the wall

apostol's calculus also has a rigorous approach but slightly less harder than spivak from what I've heard

differential and integral calculus by courant is pretty good

then you have the stand Thomas's calculus or stewarts calculus

Paul's online maths notes for calculus are greats

[gray gazelle]

HI guys im looking for a book in topology and 3d spaces, and foundations and chaos and dynamical systems

i want it to abstract the grocery lists as much as possible and sum up materiel and become from beginner to expert

qualitatevly least quantitve as possible, as least verbouse and sperflous

[jaunty quail]

I dont know much about chaos and dynamical systems

But steven strogatz as a book on nonlinear dynamics that is popular

[gray gazelle]

Full math major books list?

[jaunty quail]

For topology I recommend Munkres’s topology, treat it like a bible

I would first suggest Munkres

While reading munkres go through paul online math notes

And sometime when you feel comfortable enough start with nonlinear dynamics

You dont need to finish any of these books if you dont want

[gray gazelle]

i looked but it doesnt seem fitting what i mentioned

[trim kayak]

Where did everyone go?

[molten mason]

https://raw.githubusercontent.com/TalalAlrawajfeh/mathematics-roadmap/master/mathematics-roadmap.jpg

[molten mason]

Probably #discussion

[trim kayak]

Ooohh that's a cool document. I made it bigger to read the font and now I can't see what it says at the top.

[molten mason]

When you click it to zoom in, you sould be able to use the scroll bars to move around

[molten mason]

Springer finally sent me an official invoice right now and adjusted the charge to my card (2 weeks after original online order)

On the invoice I'm missing 2 of the books (equal to the adjustment of charge)

Is it safe to say that Springer canceled a portion of my order, or should I maybe expect them to re-charge and send a second invoice for the other 2 books?

[remote sparrow]

have you emailed customer service?

[molten mason]

No this just happened like 90 seconds before I posted in here lol

And I don't feel like dealing with customer service in the middle of the night

Just curious before I call tomorrow

[rose geyser]

can anyone recommend a combinatorics book that isn’t targeted for absolute beginners.

I’ve worked through most main problems of chapters 3-8 of A Walk through combinatorics by Miklos Bona. I’m mainly interested in partition problems, problems concerning both kinds of Stirling numbers, and using ordinary/exponential gen functions.

Would of course would appreciate if the book contained other topics.

[remote sparrow]

https://www.routledge.com/Introduction-to-Enumerative-and-Analytic-Combinatorics/Bona/p/book/9781482249095

https://www.amazon.com/generatingfunctionology-Third-Herbert-S-Wilf-dp-1568812795/dp/1568812795/

[rose geyser]

thank you book-recommendations citizen

[rose geyser]

Any opinion on A Course in combinatorics by van lint?

[remote sparrow]

https://maa.org/press/maa-reviews/a-course-in-combinatorics

looks okay

but it seems to be an introduction?

actually the exposition seems a little more sophisticated

sure, van lint is a good next step

[rose geyser]

I stopped bona in the graph theory part because I’m not interested in pure graph theory atm, my university has a good course on it and would rather wait for that first then study from comprehensive book like diestel

[strange vector]

https://www.amazon.com/Combinatorics-Techniques-Algorithms-Peter-Cameron/dp/0521457610

nice combinatorics book

[remote sparrow]

an advanced book series would be Enumerative Combinatorics volumes 1 and 2 by richard stanley

[tawny copper]

You can also look at the books of Pranav Sriram and Pablo Soberon

[rose geyser]

I’d love to use Stanley, if only I could recognise half of the words on the table of contents

[surreal depot]

are there any good cheap textbooks on mechanics

[tawny copper]

What are books that focus specifically on algebras? I am loooking for basic theory (would get over it quickly) and more advanced topics (like Azumaya algebras and co-homological methods). The thing is, I don't really have a picture of the landscape of algebras

[golden dagger]

giys

can i go from serge lang basic maths -> baby rudin

[daring lake]

will be hard i think

though you can give it a try

read a chapter. If you can comprehend most of it and solve some exercise problems, good, continue. Else, go for something gentler.

[gray gazelle]

rudin is more of a second course type material

[cunning mirage]

hey guys can anyone recommend be books for JEE prep ? maths?
like i have topics such as coordinate geometry , limits derivatives , quadratic , p and C , calculus etc-
the books should contain atleast some topics mentioned above :--) (adv level book 😏 )

[strange vector]

i think you should read at least one calculus book before reading rudin, like Spivak or Apostol's calculus. You can do it without them but i think it would be very difficult

[floral quest]

can you give an example?

[vital bane]

not really

calculus isn't necessary to study analysis

you learn everything you'd learn in a calculus book from analysis books anyway

it's just that now it's in a mathematically rigorous, step by step manner

[strange vector]

i said it would be easier if you read some calculus book before rudin. didnt said you can't do it without reading calculus

[vital bane]

you said it would be "very difficult"

which is very untrue

my calculus knowledge has NOT helped me in real analysis

it's a completely different skill set

I mean of course it doesn't hurt to know calculus before analysis, but it would certainly not be "very difficult" to study analysis without knowing calculus

[bright vortex]

hey so I recently finished watching a youtube course on number theory (As I had no idea where else to go to learn it) But I would like to see if their is a book of some kind that I can read on it because I struggled to retain most of what the guy said. (Sorry didn't mean to interrupt your convo)

[strange vector]

its not some random analysis book im talking for rudin

and you studied calculus before analysis so idk

[gray gazelle]

apostol calculus is basically intro analysis

same goes for spivak

[jaunty quail]

This is pretty good

[sage python]

Try "Number Theory for Beginners" by Weil

[jaunty quail]

I just recognize a lot of names of some of these books

[sage python]

It feels a bit too convoluted somehow. I guess it's like, common math major class dependencies and relevant books

[jaunty quail]

Oh the dependencies idc about

Its arbitrary

A lot of those books ive seen as standard in courses

Or as suggestions

[sage python]

What's your current background?

[gray gazelle]

cs

junior

[sage python]

What math have you done?

[remote sparrow]

hmm, i also just received an email from springer last night with an invoice attached, and one of my books is missing

[foggy fiber]

Is there such a thing? We can give you a list of courses / topics most math majors are familiar with, but the books used will be all over the spectrum.

[dusk wind]

there is https://realnotcomplex.com but varied

[celest bear]

Thomas’ calculus or calculus by Stewart?

[dusk wind]

try Leithold instead

[foggy fiber]

If you're just trying to learn and it's your first exposure, either will work as they have tons of practice problems. Even better is that solutions can be found online for nearly all the problems in those texts. If you want something more rigorous, then look elsewhere.

[graceful moon]

Happened to me too, there’s apparently massive backlogs at some printers so they’re shipping in like batches

I got 2 of mine and the other will be coming soon apparently

[sudden kindle]

Any recommendations to learn Patterson-Sullivan theory?

[celest bear]

Will do. Thanks

[celest bear]

I’ll look into it

[foggy fiber]

Without knowing your level of mathematical maturity, start here: https://www.math.u-bordeaux.fr/~jquint/publications/courszurich.pdf

[sudden kindle]

Thanks

[gray gazelle]

Any recommendations to learn linear algebra in depth?

[remote sparrow]

how deep are we talking here

and what do you hope to learn

[trail hemlock]

"how deep are we talking here" is kinda crazy ngl

oh shit sry for the ping

[remote sparrow]

🤨

what is bro thinking

[crimson leaf]

This is how mine went it sucks they don't tell you what's in the package till afterwards lol

[remote sparrow]

ye, thankfully it's only one book

might be shipped separately

[crimson leaf]

They did all end up coming though

[maiden halo]

does it bug anyone else that they keep changing the cover designs (for a given series)

[remote sparrow]

[remote sparrow]

not really

[left cloud]

damn i have a copy of davenport i'm never going to open i would have given it to you

[crimson leaf]

The only thing that bugs me is the spines

[gray gazelle]

Hello.
I am currently using "How to prove it a structural approach" by velleman book for proof writing. Is it worthy to have a copy of "proofs from The Book"?

[crimson leaf]

Like on Davenport they the third edition is like halfway on the spine

[crimson leaf]

It's a fun book but you probably won't be learning stuff out of it

[remote sparrow]

show us a picture

[crimson leaf]

I left davenport at home this semester

[gray gazelle]

Oh I understood.

Thanks

[crimson leaf]

I can show you Humphreys though

[remote sparrow]

i mean it was cheap i guess

[gray gazelle]

Have you guys really read these books?
Here I can't even do half of Velleman's book hehe

[remote sparrow]

no he just ordered new books from the sale last month

[gray gazelle]

Oh I got it.

[crimson leaf]

No the only ones I've read parts of or started is complex analysis and algebra by Hungerford I've also read some proofs from THE BOOK

This spine was done very well though

[gray gazelle]

Now I understood

[crimson leaf]

I plan to read part of Humphreys next semester for a direct study in rep theory though

This is like the current stuff I'm reading

[remote sparrow]

is that blue book ahlfors

[crimson leaf]

Yeah

[remote sparrow]

i heard marshall was neat

starts with power series

[crimson leaf]

I got it from a prof who was cleaning out books

[remote sparrow]

[crimson leaf]

This is like my at school bookshelf

[rose geyser]

Damn

what’s your expected duration of reading all those books?

[crimson leaf]

Probably 1-2 years if I'm lucky lol (Note I do no plan on reading every book cover to cover)

[gray gazelle]

yeah a list would be great

[gray gazelle]

Not much
Just up to calc 2 like 3 years ago

[sage python]

Okay so you'll want some proof background, some linear algebra, and real analysis

[crimson leaf]

Ooo the Dami curriculum, this is gonna be one for the pins right here

[gray gazelle]

I want to like make an accelerated plan for completing whole syllabus in a month

[sage python]

Whole math major syllabus in a month?

Yeah not gonna happen

[gray gazelle]

at least half

[sage python]

Still not likely to happen

[gray gazelle]

first couple years seems to be easy

[gray gazelle]

meh ill try

[sage python]

I'll give you three books to try

Artin Algebra
Schroder Real Analysis

Just those two for now actually

I was gonna tack on Bredon Topology and Geometry but

[crimson leaf]

Artin is really a two for one anyways

[sage python]

That's for after these two

[sage python]

Kinda why I included it

[gray gazelle]

Can I start with that one?

[remote sparrow]

https://sheafification.com/the-fast-track/

not even the fast track says you can do it in a month

[gray gazelle]

I was told this is a joke

[remote sparrow]

and it's a complete joke list

[gray gazelle]

why

like will it not work?

[crimson leaf]

This list is heavily skewed towards one part of math and makes a lot of non standard choice on how to approach the material

[crimson leaf]

Is Bredon that readable btw?

[heady ember]

I find it difficult to believe one could even finish half of any of these books in a month.

[crimson leaf]

I could see half of Schroder in a month but Schroder is very kind imo

[heady ember]

If you think you can complete the whole of a ug math degree in a month, I think that's just extremely unlikely, at the very least.

[crimson leaf]

It is kinda big though

[remote sparrow]

that's what she said

[gray gazelle]

I kinda have an exam covering it whole in a month lol

[sage python]

Bredon is decent imo

[crimson leaf]

What exam?

[heady ember]

I spent a couple of months on it already and I've still at the chapter on the riemann integral lol

[sage python]

But yeah Schroder + Artin + Bredon gives you an undergrad math major education modulo maybe some holes

[crimson leaf]

I got to chapter 4 in about a month

[gray gazelle]

It's a national entrance exam

[heady ember]

To be fair, the way I did it up to this point was to prove every claim the author makes myself + most exercises

[remote sparrow]

national entrance exam? is this a yearly thing?

[crimson leaf]

Yeah I know lol I did not do that obviously

[remote sparrow]

it would be advisable to wait another year for this sort of thing

[gray gazelle]

Although I don't wanna get into university i wanna do well

[crimson leaf]

Idk if I could do that really for most analysis books as there's some weird proofs like that proof I'm currently trying to understand

[heady ember]

Did you do anal before?

[remote sparrow]

i imagine most people on this server do not have a partner to begin with

[crimson leaf]

No but I had done other math like first 6 chapters of D&F, Graph theory, FIS, and some combinatorics stuff

[gray gazelle]

I hope to learn the concepts from zero, i just know about SEL and matrices

[heady ember]

To complete chapter 4 in a month, 100/30 ~ 3.3 pages a day . Ok that doesn't seem to bad now that I notice this

[remote sparrow]

what's "SEL?"

[heady ember]

I see

[crimson leaf]

I did not complete Chapter 4

[heady ember]

My personal background was that I completed the whole of Enderton

[crimson leaf]

I actually stopped using it because my professor was using a different book and the content did not match up very well so I switched to his book

[heady ember]

I see

[gray gazelle]

Oh I'm sorry, systems of linear equations

[crimson leaf]

Mainly we were doing topology on R and building everything from that instead of Cauchy sequences

[tawny copper]

@heady ember is your main focus set theory/logic?

[heady ember]

Yes and no. Yes because currently the field/topic I have the most interest in is indeed sey theory. No because I still need and want to explore other areas in math.

[remote sparrow]

so you've learned some linear algebra before?

[heady ember]

Like maybe DG or AG, eventually

[crimson leaf]

What about model theory

[remote sparrow]

need algebra

[heady ember]

I'm just gonna learn enough mathematical logic to do more set theory first

[crimson leaf]

Yeah isn't it based on universal algebra

[remote sparrow]

i mean i guess there's some ug model theory books like kirby

i heard about it from peter smith's list

[gray gazelle]

Yup, discuss systems with parameters, etc

The basics

[remote sparrow]

try Linear Algebra Done Right

[heady ember]

Friedberg has been good in my exp

[tawny copper]

Model theory? No

[heady ember]

Use his latest ed with the updated chapter on 's (dets)

[crimson leaf]

Huh, where does it come from then?

[remote sparrow]

i think you may have been thinking of a pithy, but not necessarily very accurate, quote from hodges' model theory book

[tawny copper]

But algebra is just a very rich source of models, that's what Sour Drop meant presumably

[gray gazelle]

Hmm I don't know about vector spaces

[crimson leaf]

Maybe, I read it somewhere online one time

[remote sparrow]

#book-recommendations message

these are good beginner books

[heady ember]

I stan friedberg (because I used it , but jokes aside its very gentle)

[gray gazelle]

Thank you!

[heady ember]

Also check pinned for Dami's lin alg book review

[sage python]

Yeah FIS seems like the standard pick nowadays

[heady ember]

Speaking of the devil

[crimson leaf]

I do really like FIS

[sage python]

And what I'll probably recommend to that one guy when his plan to learn everything in a month burns to the ground

[crimson leaf]

It's really good for beginners the writing is very easy to digest and the exercises are a good amount of difficulty

[sage python]

Yeah FIS might be the best linear algebra book right now tbh

[tawny copper]

It simply naturally arises from logical considerations. Like how to prove some propodition is not true "in general" it suffices to show some example (i.e., a model) where it doesn't hold

[sage python]

From TAing from it once it seems to do both theory and the needed computations

And it's written easily so it can also double on as your first intro to proofs

[tawny copper]

In the definition of what it means for a formula to be "true" you already use models, or at least that's what I have seen

[crimson leaf]

I also TA'd a course using it and yeah the text makes it really easy to explain problems or give hints as well

[remote sparrow]

most introductions to mathematical logic do a little bit of model theory

[crimson leaf]

I'm ngl some of the logic stuff seems really cool (like this talk on NSA I went to) but it is probably the quickest thing to lose my interest as well

[remote sparrow]

what is NSA

[crimson leaf]

non standard analysis

[heady ember]

Ah Sharp's beloved

[tawny copper]

There is a proof of Szemeredis theorem that uses model theory stuff, although I haven't read it yet. The author claims it's the correct approach.

But I think the model theory going on in such applications is not super sophisticated (compared to "pure" model theory)

[crimson leaf]

Was it the one by Renling Jin?

It was his talk at Integers I went to actually

[tawny copper]

Yes

I mean, idk if it uses novel ideas (compared to other proofs) or if it's just using another language. Either way it's interesting

[tawny copper]

That sounds cool

[crimson leaf]

It was on a different topic, https://events.dm.unipi.it/event/151/contributions/339/attachments/79/103/Jin.pdf but he was talking about that paper very excitedly with the additive combinatorics peopel from UGA

[tawny copper]

Thanks for the link

[signal tiger]

Any book recommendation for probability and statistics? I need to learn it as those are basics of machine learning

[remote sparrow]

calculus-based?

[signal tiger]

yes

[remote sparrow]

https://stat110.net/

https://www.amazon.com/Mathematical-Statistics-Applications-Dennis-Wackerly/dp/0495110817

[signal tiger]

🙏thx

[gray gazelle]

Couldn't find Schroder Analysis book anywhere

[heady ember]

https://www.amazon.com/Mathematical-Analysis-Introduction-Bernd-Schröder/dp/0470107960

[gray gazelle]

Is this the correct book?

Doest say Real Analysis

[daring lake]

mathematical analysis typically covers real analysis in a more general way (and some elements from complex analysis)

i had a look at index and chap 1-7,10,11,12 would typically be done as a first course

[dusk wind]

Imagine having to hunt down the latest edition of a book

[sage python]

Yeah that's the right one

It's about real analysis even if it's called mathematical analysis

[autumn quartz]

Recommend books to manipulate others

[marsh ingot]

[gray gazelle]

11th grade maths book ig

[sudden kindle]

Thats a zemon moment

[oblique mica]

Any resource recommendations of fine moduli space for researchers in engineering?

[cyan scroll]

Hi, everyone can someone recommend a book about field theory and Galois theory? I would like a book that explains the theories and their implecations(or how to use them)

[remote sparrow]

https://www.amazon.com/Galois-Theory-David-Cox/dp/1118072057

[mossy flume]

David Cox 💯

[cyan scroll]

Thx will check it out

[thorn cloak]

Has anyone used 'an intro to stochastic modeling' by Taylor? Wondering if it's good for stochastic processes or If there is a good supplement

[molten mason]

+1 to Linear Algebra by Friedberg, Insel, and Spence. 5th edition is $30 USD on Amazon.

Linear Algebra Done Right, 4th edition by Axler is available legally and free online on his website.

Both are great books, recommended by a good majority, feel free to use both.

[cold shore]

I am trying to learn real analysis, and my professor told me Rudin's books are good

I found there is 2 of them and which one should I get?

I think one is Principles of Mathematical analysis and the other is Real and complex analysis

[sage python]

If you're learning undergrad level real analysis

Then "Principles of Mathematical Analysis" is what you want

[lime vessel]

The order of Rudin's books is PMA -> RCA -> FA

[primal mica]

I was looking for a book similar to Matrix Analysis by Horn, but since I am a physicist I prefer picture books like Clifford the Big Red Dog. I can already apply many of the concepts covered in this text, but I am trying to rebuild my foundations with more geometric intuition.

Does anyone have a recommendation for a less rigorous and more geometric/pictorial presentation of these topics?

[stark bone]

Hello, are there any recommended yt videos or courses on Abstract Algebra?

[tawny copper]

Benedict Gross

Covers Artin's book (not all) so you could read that book along side

[stark bone]

Thanks

[autumn relic]

Hello, can anyone recommend a book(s) for introductory differential equations suitable for self-study?

[stark bone]

@tawny copper Is it an introductory course?

[tawny copper]

yes

I can even tell you that some of the students that actually took that class didn't know vector spaces nor modular arithmetic

[graceful moon]

Also recommending Artin, a much more enjoyable read than DF imo

[finite gale]

Anything that isn't d&f is probably a better reading experience than d&f

D&f will cover what you want to cover but do so in a very wordy manner

[vital bane]

wordy is enjoyable

[dusk wind]

to the layman

[finite gale]

Maybe if you have a daily quota of words read

[dusk wind]

around 100

[gray jungle]

Richard Borcherds has multiple incredible series on Algebra

[grim sinew]

Percy Jackson

[scarlet steeple]

I want to read Advanced Calculus: A Geometric View by James Callahan, is it a good book for those whom read it?

[viscid frigate]

Hello! Can I get some Youtube video recommendations on Algebra 1?

[stuck zephyr]

khan academy

[viscid frigate]

okay, thanks!

[strong stream]

has anyone here read Flatland: A Romance of Many Dimensions and how good is it

it's an old fiction apparently

[modern ruin]

I LOVE THIS BOOK

[strong stream]

the only thing I know about it is terence tao read it when he was like 9

[modern ruin]

if you read it you'll know more about it

[vital bane]

it's crazy how that works

you read a book and you know more about it

damn

[strong stream]

amazing

[vital bane]

Richard Borcherds has a based af channel

so many lecture series on lots of different stuff

undergrad algebra, comm alg, alg geo

number theory

based

[arctic hamlet]

Do you guys have any recommendations for calc 2? I need a book has clear explanation and tons of examples. Thank you first.

[vital bane]

spivak?

[scarlet steeple]

youtube and khan academy is your best bet

[scarlet steeple]

bro

[vital bane]

spivak's "calculus" lol not his CoM book

[scarlet steeple]

oh 💀

isnt it rigourous calc tho?

with proofs n stuff

[vital bane]

nah

not too many proofs

Like it's not an analysis book

but it is a bit more rigorous than just a basic calculus course

[vital bane]

try looking at spivak, it you dont like it then khan academy is very good

it's where I learned calc

even learned calc 3 using that

[arctic hamlet]

Ty you guys, was lost at my first calc2 class maybe will try a combination of khan academy and textbook

[vital bane]

yes that's a good idea

[rigid barn]

Why is D&F so hated on. Granted I never read much of it, but what little i did back when I knew very little felt like a very pleasant, paced read. Wordy is not so bad for a beginner imo. That said I would never personally recommend D&F, I think there are far better alternatives.

[finite gale]

I used to like d&f but that was because that is what I used to learn in undergrad

Then I tried other texts and found the writing in other books just felt nicer to read

In particular, I think rotman is quite nice

[rigid barn]

I think you're ignoring the fact that you knew more at that point. D&F very quickly loses relevance once you're past the basics of the subject.

[rigid barn]

I like Rotman too. Not my favourite, but it's pretty well written. If I were doing tier-lists I'd rate it as S or A or w/e.

[modern ruin]

it's BORING

(half joke)

I don't actually hate DF

but it's really fun to hate on because I just love Aluffi so much

[rigid barn]

now here's a good target for hate

[modern ruin]

no way

[arctic hamlet]

now I wonder what is DF? differentiate function?

[strange vector]

Aluffi's algebra notes from underground is so wordy tho

[strange vector]

Dummit Foote's abstract algebra book

[rigid barn]

He probably means Meme0

[mossy flume]

D&F is too verbose for me

very boring to read

[strange vector]

i think its good for reference

[loud cradle]

i agree, it has many good examples and exercises but the exposition is very dull

makes algebra seem like a very boring subject

[mossy flume]

it's a great reference for sure

I have a copy for reference

for learning algebra the first time, theres better

[rigid barn]

I'm not defending D&F because I like it so much, but I do think the haters speak from the vantage of experience (now D&F is boring to us).

[mossy flume]

yea I mean I didn't use a text when I was first learning algebra (just whatever notes my prof had)

so that is a point

[loud cradle]

it was the nominal textbook when i first learned algebra but the prof never referred to it once haha

i'm still glad to have it as a reference though

[rigid barn]

Yep, my entire D&F apologia rests on that.

[crimson leaf]

We used D&F in our intro algebra it was good enough I do feel like sometimes the examples are a bit too much though like for instance you start Euclidean Domains you get the definition and a bit of motivation then like 2 pages of examples. I also didn't like some of the organization in part 1 such as in chapter 1 they introduce group actions and then pretty much ignore them until chapter 4. This wouldn't have been a problem to except it felt they expected the reader to carry the information from chapter 1 with them iirc they don't even recall what a group action is they just tell you to read 1.7 again which to me just seems like poor planning.

[remote sparrow]

for example?

[remote sparrow]

examples?

[rigid barn]

Isaacs or Jacobson or Rotman or Knapp (admittedly a little tougher than D&F).

[mossy flume]

Rotman

[remote sparrow]

which rotman

he has an undergrad and a grad book

[mossy flume]

A first course

[rigid barn]

I'd actually recommend the "grad" book, Advanced Modern Algebra.

It's a meaningless distinction anyway.

[mossy flume]

Ehhhh I think that'd be fast for someone who has literally never seen algebra past LA

[remote sparrow]

https://www.amazon.com/Basic-Abstract-Algebra-P-B-Bhattacharya/dp/0521466296/

i heard this was good

[rigid barn]

Well it depends who we're advising, for a slightly experienced person I'd recommend what I said.

I'd even recommend Lorenz' Algebra 1, which explicitly assumes nothing beyond LA, same as Jacobson1.

[mossy flume]

wait we're talking about first algebra texts

[rigid barn]

But yes, these books are somewhat tougher than Fraleigh or w/e else.

[mossy flume]

like never seen anything past LA

wait no I forgot my favorite text how could I

Artin

Artin is fantastic

[rigid barn]

I'd rate it about the same as D&F.

[mossy flume]

really?

[rigid barn]

It's shorter, but it covers less too.

[mossy flume]

I find Artin's writing to be better

well yea it's a first course

[rigid barn]

Oh the writing is better, I agree.

But these aren't novels.

[mossy flume]

it matters alot lol

[rigid barn]

In any case, if we're talking absolute absolute beginners I'd recommend Vinberg. Like Artin, but cooler.

I do give Artin points for how massively varied he is for an intro book.

[molten mason]

Howard Anton has a good calc book with tons of examples and problems.

[arctic hamlet]

will give it a look, tysm

[autumn spire]

hello

can someone recommend me good question bank books for olympiads

for ioqm and stuff

[narrow prairie]

Anything by titu andreescu

Also join https://discord.com/invite/mods

[vital bane]

[silent edge]

why is the link called mods

[cold elbow]

cuz why not

[finite gale]

#competition-math

[meager socket]

would you all reccomend hall and knight higher algebra for someone who is in pre calc
the second example worked out took me ~45 minutes to figure it out and i think that's way too slow for such a simple problem so i don't know if i'm good enough for the book

[molten mason]

Lmao I don't have picture privs in this server

My Springer books finally arrived.

My initial review is the Springer hardcover spines aren't even attached to the pages. They're just floating. Which I've read before is a common complaint

[remote sparrow]

yes, they basically paperbacks with a cardboard cover

[molten mason]

Hard to complain for a $20 book

[mossy flume]

Math Olympiad Discord Server

What's a representation theory text that covers the Schur-Weyl duality?

It doesn't seem like Serre's lin reps text covers it

Does Fulton, Harris cover it? I don't see Schur-Weyl in the index

[crimson leaf]

According to wikipedia and ncatlab it should

[mossy flume]

oh hm ok

[crimson leaf]

My internet died for a bit but it looks like section 6.1 and 6.2

[gray gazelle]

that's an old and outdated book with no return value whatsoever

pick up a normal and modern pre-calc book and supplement it with khan academy

https://openstax.org/details/books/precalculus-2e

[vapid sedge]

someone have Caluclus 1 from Guidorizzi?

[strange vector]

Yes, it's a nice book but if it takes too long to do exercises, you can read Algebra by Israel M. Gelfand first.

[pliant wadi]

Is representation theory for finite groups by Martin Barrow a good book for a beginner who's done courses in group theory, linear algebra and rings and modules?

If not, are there any good alternatives?

[silk apex]

I wanna read one or two Sigmund Freud books, if anyone has read, what would you recommend to begin with?

[vital bane]

$20 is insane man 💀

that aint cheap

[earnest wolf]

https://amzn.eu/d/cK3Mtp0 💀

(most textbooks can be found online tho xD)

[strange vector]

any recommendation for rigorous set theory books? I have Thomas, Jech Introduction to set theory and Enderton's elements of set theory but i don't like both

[heady ember]

What do you not like about them

[strange vector]

Jech and Thomas lacks formalism

enderton is nice but don't like his style that much

I read Naive set theory by halmos too but looking for more advanced

[heady ember]

Why don't you like his style

[heady ember]

Huh? Wdym

[strange vector]

Jech and Thomas says even in preface, if you are looking for formal representation, read a logic book

and enderton is not consistent at some places like he says we are dealing only with sets and elements of these sets are themselves sets, then constructs a set like {1,2,3}

[vital bane]

then read Jech grad book

[heady ember]

{1,2,3} is a set of sets...

[strange vector]

we did not defined numbers as sets at that point

[heady ember]

Is that chapter 0?

more accurately ch 1

[strange vector]

i guess

[heady ember]

...

[vital bane]

[heady ember]

ch 1 is meant to give a naive intro and provide some motivation...

[heady ember]

Why is it not formal enough for your needs

[strange vector]

nope it says formal

not naive

[heady ember]

On ch 1?

[strange vector]

i like formalism

[heady ember]

🗿 Everything else is formal enough, at least to the same degree as jech's ug book.

Using some context should tell you that ch 1 is giving motivation...

[strange vector]

jech's book is not formal did you read it?

[heady ember]

Have you read a book on mathematical logic? If not I doubt you'd be able to read a grad set theory text.

[vital bane]

what is not formal about Jech's book?

[strange vector]

idk authors themselves says its not a formal text

[vital bane]

bruh

[heady ember]

Bruh

You claim to have seen jech's text & thinks is not formal enough for your needs

Yet you haven't read it

[strange vector]

i read it

2. The treatment is not formal. Logical apparatus is kept to a minimum
   and logical formalism is completely avoided

from preface

[vital bane]

you mean you read the preface

[heady ember]

Then, do you mind providing an example of why it isn't formal enough for your needs

[vital bane]

What even is logical formalism? instead of using words using for and?

[heady ember]

Initially I thought you read the book and you were referring to something like his use of class functions, e.g. in transfinite recursion. But go into a grad set theory book and you'll find the same paraphrasing.

[vital bane]

Like principia mathematica proving 1 + 1 = 2?

[strange vector]

sure

are there anyone who knows what formal book looks like can suggest a set theory book?

[heady ember]

sigh

[strange vector]

its book recommendation channel

[vital bane]

now you understand what normal mathematicians feel when talking to set theorists

[dusk wind]

whats set theory

[tawny copper]

@strange vector I think Tourlakis' books are pretty formal Lectures in logic and set theory, specially the first volume

but I don't see the problem with Jech's third millenium book

[molten temple]

jech is pretty damn formal

[strange vector]

thanks, i was talking about jech's introducrion to set theory

set theory is another book

[tawny copper]

I cannot talk for that one. But the other Jech book is pretty nice I think

[heady ember]

I think Jech's ug book should be about the same formal as his grad book, in the stuff they cover in common like transfinite recursion.

[glossy zealot]

I think grass has proven from time to time that he has the credentials regarding book recommendation. Were I to disagree with him, I would try to explain my reasons further because I know he is trying to help. I hope we can all have a positive attitude

[pliant wadi]

Is representation theory for finite groups by Martin Burrow a good book for a beginner who's done courses in group theory, linear algebra and rings and modules?
If not, are there any good alternatives?

[steel cloud]

Any recommendation for logic and set theory?

[molten mason]

Have you read Naive Set Theory by Halmos?

Or do you need something more formal

[strange vector]

for logic im currrently reading principles of mathematical logic by David hilbert, its really good so far. for set theory intro, naive set theory by halmos is nice

[remote sparrow]

why make the complaint that hrbacek and jech is "informal" but not make the same complaint about enderton? because one book explicitly states it does not formalize its axioms in first-order logic? neither assume prior study of mathematical logic, which is what makes their treatment "informal." however, both have an axiomatic approach, which sets them apart from books like halmos.

https://maa.org/press/maa-reviews/introduction-to-set-theory

hrbacek and jech is a perfectly acceptable book. you can read kunen or big jech later

[strange vector]

because jech's book is not formal, even jech says its not a formal treatment

why so mad tho, is not being formal bad?

jech says this at preface: 2. The treatment is not formal. Logical apparatus is kept to a minimum
and logical formalism is completely avoided.

The treatment is not formal

from the book: Our exposition in this section is informal. Readers who would like to see
how this topic can be studied from a more rigorous point of view can consult
some book on mathematical logic

that's so funny that everyone saying the book is formal but writers of the book says it's not

[remote sparrow]

enderton is not a "formal" treatment either. both enderton and hrbacek/jech are the exact same style of book. they aim to teach axiomatic set theory without requiring prior study of mathematical logic. neither review or introduce any sort of mathematical logic. they both rely on your intuitive notions of logic. but the axioms are all there! hrbacek/jech, to reiterate, is not at all in the same class as a book like Naive Set Theory by halmos. that is what is meant when hrbacek/jech means when they state their book is not "formal" as compared to a book like Basic Set Theory by levy, Set Theory by kunen, or Introduction to Axiomatic Set Theory by takeuti and zaring.

[strange vector]

yes i'm not saying enderton is formal too but compared to jech, its more formal

jech using almost only english words for definitions and theorems

i'm saying it's not formal i don't know what is the issue here.

[remote sparrow]

exactly what is your impression based on? you aren't going off of much besides the preface, and you seem to have a very different interpretation of "formal" than the authors and people familiar with how set theory is taught do. what is "formal" to you that makes enderton more formal than hrbacek/jech? that enderton uses unexplained logical symbolism more often?

[strange vector]

jech uses much more english words instead of symbols

like halmos

[remote sparrow]

A Friendly Introduction to Mathematical Logic by leary and kristiansen and Elements of Set Theory by enderton are good. Classic Set Theory by goldrei is good too

i'd probably read Propositional and Predicate Calculus: A Model of Argument by goldrei if you're curious about propositional logic specifically, since leary and kristiansen jumps right into first-order logic. it's not wrong, since first-order logic subsumes propositional logic, but propositional logic gets more attention from computer scientists than mathematicians give it as far as i've heard. chapter 1 of Introduction to Mathematical Logic by mendelson is pretty decent too.

[steel cloud]

No I didn't read Naive set theory

[gray jungle]

What exactly is formal to you ? using more symbols doesn't make something more "formal" , this is not the difference between naive set theory and formal set theory.

any graduate set theory book will be formal

unless we have different definitions for it

[strange vector]

we have different definitions

using symbols instead of words makes the text more formal look up for the books that accepted as formal

i didnt say anything about naive and formal set theory where that came from?

[gray jungle]

I suspect what you are looking for is not a "formal set theory" book you are looking for a set theory book that's not verbose, jech grad book is considered formal altho it seems too verbose for you it seems.

[strange vector]

yes, that is what i'm saying.

its jech's undergrad book btw. The book i'm talking about is intoduction to set theory, not set theory by jech

[gray jungle]

fair enough, unfortunately i only used halmos for naive set theory so i cant recommend anything else.

[vital bane]

naive gang

[remote sparrow]

i'm rather disappointed that the fourth edition of LADR is perfect bound as a single text block rather than in signatures

my third edition was bound much more nicely

Measure, Integration, and Real Analysis is made much better, as i had hoped

[dusk wind]

what is set theory?

[woven latch]

Looking for books about Digital Signal Processing. I've gone through Discrete-Time Signal Processing by Alan Oppenheim. Seeing if anyone has a good follow up recommendation

[heady ember]

I think I got a bit irritated because

1. You seemed to ignore what I was saying, just repeating that things aren't formal. E.g. When I told you Enderton's first chapter is meant to provide intuition, you simply restated that it was supposed to be formal.

2. I don't think I said either are formal. Reading carefully, I believe one should find that I used "formal enough".

3. You seem to not know what you want. You keep stating you want a formal treatment, yet you can't give an example of why things aren't sufficiently formal. Similarly, you claimed to have read the books, when it seems you have only read the preface.

4. Your tone didn't seem, at least to me, to be the most polite. E.g.:

ch 1 is meant to give a naive intro and provide some motivation...

nope it says formal
not naive
The way you phrased it makes it seem like you're not even respecting what I'm saying. To an extent, it feels that you aren't even listening.

[candid sequoia]

Hi I want to expand my knowledge in maths any book recommendations? Note: I am in 9th grade.

[crimson leaf]

I would recommend Khan academy

[crimson leaf]

Well if you keep reading (which I assume you did) you'd notice op was not using formal correctly anyways

[candid sequoia]

I find the website really confusing

[crimson leaf]

Which part of it?

[vital bane]

signatures?

[candid sequoia]

The lectures

Ima have to just get used to it

[remote sparrow]

sometimes a large book is "subdivided" into little booklets. imagine a piece of paper. fold it. get another piece of paper and fold it. put it inside the folds of the previously folded page. repeat this process for some more pages. this is a signature. you can stack other signatures and glue or sew them together.

one of the big advantages of this construction is that the books lay open flat a lot more easily.

[vital bane]

man I must've gotten scammed cuz the copy of LADR i got (like a year ago) the signatures were all over the place not at all aligned

and it was in black and white

on amazon

[remote sparrow]

[vital bane]

I hope the other books I purchase will actually be a good quality product

[heady ember]

Yeah I had a feeling that he didn't exactly mean formal

[fierce hedge]

Why not just get it printed, I got it printed on A4 paper and it looks glorious

[crimson leaf]

Well like where would you get it printed and if you did how somewhere how would the legality of that work since it's technically copyrighted right?

[fierce hedge]

It doesn't matter in the 3rd world country I and neam live in so it works out but yeah even though 4th edition is open access printing the book is technically piracy.

By doesn't matter I mean the chances of getting prosecuted to that are negligence

[gray gazelle]

Is Lee a suitable replacement for Munkres for learning point-set topology?

[crimson leaf]

Ah yeah, I wish we could do that idek where I would get a book printed and bound to begin with

[fierce hedge]

There are technical loopholes around this like you can print a part of the book as teaching material and part by part get the whole book printed.

[vital bane]

where

[fierce hedge]

Printster

[vital bane]

it's more of a topological manifolds book

rather than studying general topological spaces

But if you plan to do diff geo/diff top then lee would be sufficient

[vital bane]

will the police come to my house if I print a pdf

[remote sparrow]

do the police have the resources to go after someone printing a pdf

you're not running a printing empire

[fierce hedge]

Lmao no, I once even contacted the authors of a CS book asking if I could print their book cause it was out of print here. They said no but I printed it anyway

[tawny copper]

depends if you are white or not

[crimson leaf]

Hmmm actually I wonder how expensive it would be to use prinster and some kind of 3rd party shipping agent so have prinster send it to the shipper then to me. Of course I would only do this for books which I am legally allowed to print

[fierce hedge]

I can tell u the approximate cost if you really want to know

[crimson leaf]

Looks like 6.31 for my "thesis"

Hard cover 392 pages double side a4 paper

[tawny copper]

6.31 dollars?

[crimson leaf]

Yes USD

Then plus agent fees and shipping cost of course

[fierce hedge]

Is this for the basic paper quality

[crimson leaf]

Yeah 75 gsm normal

[tawny copper]

A4 books are annoying tho, too big

[fierce hedge]

You can also get B4

And A5 I think

[crimson leaf]

A5, A4, and B5 are all I see

A5 would be nice

[tawny copper]

where is this at? Can you send link

[remote sparrow]

https://printster.in/

indian company

[fierce hedge]

Oh yeah mb, I meant B5

[gray gazelle]

I am using "Understanding Analysis" by Abbott for self study real analysis. But, I wanna ask should I use any other book for supplementary too? If so, then which one will be suitable for me?

[rare estuary]

I have been using Spivak's Calculus and Proofs by Cummings along with Understanding Analysis

[remote sparrow]

abbott works pretty well by itself, but cummings' Real Analysis: A Long-Form Introduction pairs well with it

[rare estuary]

They seem to work well together. Spivak has different sorts of problem (both more elementary and a bit trickier) and doesn't assume that you've had calculus before. In particular, the problems from chapter 1 really got me comfortable with manipulating absolute values and inequalities. I think that's been helping with Understanding Analysis

[gray gazelle]

I see. How was your experience?
And how you used these two books as supplementary? (Meaning do you use these books for extra problems?)

[gray gazelle]

Yes indeed. Abbott's book is pretty smooth. But I thought maybe having some supplementary books may help me more.

[gray gazelle]

That's amazing. Lemme find pdf and check both the books (because unfortunately in my country these books are not available:(( )

I have also heard about the book "the way of analysis".

[remote sparrow]

iirc, there is only a really crappy scan available for Real Analysis: A Long-Form Introduction by cummings. but the book is pretty cheap on amazon.

Additional resources for Understanding Analysis by Stephen Abbott

Notes:
https://mileti.math.grinnell.edu/m317f23/Analysis.pdf

Solution manuals:
There is an official partial solutions guide available at the usual place to find free PDFs.
https://github.com/UlisseMini/understanding-analysis-solutions (unofficial full solutions manual)

Lecture playlists following the book:
https://www.youtube.com/playlist?list=PLB-Mc4u93V4WwyRck9HACF2v_Q5V0bdNJ
https://www.youtube.com/playlist?list=PLysi2xmniDSzz6xT7IzOifpoexeKccThh
https://www.youtube.com/playlist?list=PLLFpXNanTP9WGfbjxR5kCMXQgol4bGehz

[gray gazelle]

Yes. There is scan available, I am trying to make a print copy of that scan. (Amazon is not available in Pakistan too😭)

[remote sparrow]

you could try to email the author about your situation. he seems like a nice guy

[gray gazelle]

Thank you so much for this. Indeed this is helpful.

[gray gazelle]

Ok I will try. If I am not wrong then the email is
[e-mail]

[remote sparrow]

yeah

[gray gazelle]

Thank you. I will share my situation with the author

[remote sparrow]

https://www.amazon.com/Solutions-Mathematics-Universities-Qualifying-Questions/dp/9814304956

https://www.amazon.com/Berkeley-Problems-Mathematics-Problem-Books/dp/0387204296

neat books containing some qualifying exam questions

[molten mason]

There's also a UCLA Analysis Qualifying Exam Solutions pdf. Covers from 2009 to 2020

[remote sparrow]

title and author?

[molten mason]

That looks awesome, bit pricey though but I'm sure it's worth it

[molten mason]

It's the first link if you google it, from the official math.ucla.edu domain, Adam Lott

[molten mason]

I like that there's multiple solutions given for most problems

[remote sparrow]

neat

[gray gazelle]

Is it possible for me to read these books? And solve at least some problems?
I am a beginner in real analysis and proof base mathematics. Currently studying second section of second chapter (Abbott).

[strange vector]

It's not even first chapter, its chapter 4 or 5 and not for intuition read the book. and i discussed like 5 people here just tired, if someone says jech's intro set theory book is formal, send message to jech himself and let him fix his preface where he says his book is informal.

people don't even read the full conversation and thinks i'm talking about jech's set theory like wtf

i read almost half of the jech's intro to set theory book and i think i can say its not formally written, look for what formal means if you don't know. You can't write formal book just using words

[sick river]

is lee good for a second pass on topology?

[vital bane]

woahh

[vital bane]

lee's topological manifolds?

[sick river]

yeah