book-recommendations

[tawny crater]

I think the thing that will help me the most is a reference textbook because the syllabus uses specific names for anything and idk what correalates to what

[vital bane]

what kind of fourier analysis course is this?

are you using measure theory and functional analysis?

or just using the riemann integral?

[tawny crater]

its a real analysis course that does a chapter on fourier

comes before lebesgue and measure theory

[vital bane]

then have you checked out stein and shakarchi's book on fourier analysis?

[tawny crater]

ill try, thanks

the main problem is that im trying to learn the course on my own as my university teaches it and he teaches it a bit his own style so it's a bit of a glob

[vital bane]

what book is the prof following?

[tawny crater]

no idea 😄
it states that a bibliographic list will be available on moodle (it is not)

[vital bane]

have you asked the prof?

[graceful moon]

<@&268886789983436800> he’s doing this in every channel

[tawny crater]

somewhere he mentions a davidson donsig book but i find it an annoying book

yeah i was coming to that conclusion that i'll have to email him

the book writes everything in sin and cos and everything has those long engineer's formulas and it's my last resort

[vital bane]

but yea stein and shakarchi's book is like a whole book on it without using measure theory or the lebesuge integral, just like what you're doing

[tawny crater]

cool! i'm giving it a look

[fresh skiff]

I have head that this book has minimum prerequisite. Can you please tell me about the prerequisites

[tawny crater]

seems to be you need to know reimann integration

[fresh skiff]

Oh so atleast i should have knowledge of real analysis 1 and 2

[vital bane]

They talk about it in the preface

[fresh skiff]

Oh having knowledge of riemann integral is essential. So overall, this book contains its prerequisites in appendix too.

i guess I should wait untill i reach to integrals chapter of abbott

[remote vortex]

Yes, I don't see a way of doing Fourier analysis without some grasp of integration.

Unless maybe you go full abstract algebra and start talking about characters on groups

[graceful moon]

That sounds more enjoyable

[still panther]

finally, analysis for normal people

[remote vortex]

Talk about contradiction in terms

[graceful moon]

I actually should find a Fourier book because my analysis exam is on Wednesday and I’m kinda shit at it

Especially like showing things are approximations of unity and very very much Cesaro summation (not so much Fourier stuff but it was in the same section), really need more practice at those

[sturdy shore]

even in the abstract algebra route you'll need integration, I don't think you can get around the fact that the fourier transform is literally an integral (except in the finite case where integral = sum)

[fresh skiff]

Fair enough. So Abbott is enough to start Fourier analysis?

[gray gazelle]

Hello are there other good books and resources to learn Calculus and Linear algebra in parallel other than Stewart's book? I think it's a bit too long

Or is it better to do calculus + proof book like chartrand-zhang/velleman?

[vital bane]

usually linear algebra is better learnt in parallel with multivariable calculus

linear algebra looks at linear maps between vector spaces, multivariable calculus looks at non-linear maps between vector spaces...so there is a strong parallel between both subjects

even the derivative is a linear map

[gray gazelle]

Wow I had no idea

I will do basic calc + proofs then

But what is a good calculus book?

[vital bane]

ya, you can focus on doing lin alg + multivar calc in parallel

[vital bane]

if you're into proofs then spivak's "calculus" is a great book, for single variable calculus

[gray gazelle]

im not at multivar level yet

[gray gazelle]

I don't know proofs, I'm asking for introductory book on calculus, and do a proof book like velleman's how to prove it in parallel

[vital bane]

yea you can do velleman in parallel to this one

it's not like proof proofs but yk

it's more than just a simple calculus book

[gray gazelle]

Spivak assumes you are familiar with proofs before you begin the book

[tribal crow]

huh. I quite enjoyed LA without any mvc background lol

[vital bane]

I definitely don't think so lol

which spivak are you talking about?

[tribal crow]

he doesn't

[vital bane]

of course

you can enjoy either without the other but

but I'm saying mvc and LA go hand in hand

[vital bane]

he has two books

actually he has several but there are two of interest right now

"Calculus" by Michael Spivak and "Calculus on Manifolds" by Michael Spivak

the former is what I'm refering to, the latter is for later

[fresh skiff]

I believe rn she is talking about former book, the later one is at another level

[vital bane]

it's not that bad you just need to know analysis

either way Spivak's single var calc book doesn't assume proofs

[gray gazelle]

He does, from the first exercise page (exercise 20) and every exercise after this pretty much is "prove..."

There are many ways to prove as well like induction, contradiction, etc but if you are not familiar with proofs how should you know?

[vital bane]

you're right he seems to

Then you can use thomas I suppose

[gray gazelle]

Wait actually, from exercise 12 in chapter 1 and onward is pretty much just proofs

[tribal crow]

fwiw, Spivak's book was my first real intro to proofs (along with FIS)

[vital bane]

imo it doesn't really matter where you learn calculus from, I just learned from khan academy and youtube back when I was in 10th grade

[tribal crow]

I only did a bit from Velleman before that

[vital bane]

Abbott was my real intro to proofs

I actually learned how to write proofs through Abbott I didn't do a separate proofs book

[tribal crow]

his exercises are really hard at times though, so if you don't want to deal with that you can get a diff book

[tribal crow]

I liked FIS as an intro lol

[vital bane]

I just followed the advice people here gave me "you don't necessarily need a proofs book, you learn proofs by doing them"

[tribal crow]

Spivak was much more brutal

I did maybe like

30 pages in Velleman then decided it was a waste of time

[vital bane]

yea actually doing a (a good) math book is a better way to learn proofs, imo

[tribal crow]

agreed

[vital bane]

same except it wasn't velleman in my case it was "mathematical proofs a transition to advanced mathematics"

[tribal crow]

what a name lol

[gray gazelle]

that's chartrand zhang book

[vital bane]

I think so

[vital bane]

i mean

it is a based book though

like it does a some group theory, ring theory, number theory, some analysis at the end

like using the proof techniques you've learned

but I suppose it wasn't my style

I just started doing the math I wanted to do

[fresh skiff]

oh I remember last time i tried to read it (calculus on manifolds by spivik) when i didn't even started analysis

[tribal crow]

I must've tried starting CoM at least 4 times now lol

[slender cargo]

There are literally books that do both in parallel. Shifrin's book, and Hubbard and Hubbard, are the well known ones.

[vital bane]

that's like me trying to do spivak's intro to differential geometry without having done his calc on manifolds

[tribal crow]

this time is the first time I actually have the proper background now

[tribal crow]

so real

[vital bane]

she's talking about single variable calculus

[slender cargo]

Oh what

[vital bane]

Lol ye

[gray gazelle]

idk about learning proofs by doing them, you have to be familiar with them, you can't just derive proofs from thin air and you can't check for yourself if the proof is correct or if there is a simpler proof technique?

For Spivak, he gives a grand total of ONE theorem and proof before you dive into 25 exercises where 21 of them are proving things, you really think this is reasonable?

[vital bane]

then do Abbott

he teaches you how to do analysis proofs

slowly step by step

[slender cargo]

Just get his separate Answer Book to check your work.

[gray gazelle]

I don't understand what you mean

[tribal crow]

ngl, his answer book is super handwavy lol

but it's not bad

[slender cargo]

Linear Algebra comes into play with Multivariable Calculus. But you have to do the single-variable case first.

[slender cargo]

From what I've seen it gives enough detail, easily

But yeah they're not always full proofs.

Now if you're a complete badass, go learn multivariable calculus through Harold Edwards Advanced Calculus: A Differential Forms Approach

which I'm thinking of checking out

[gray gazelle]

im so confused now why are we constructing more random books and topics like real analysis, deriving from the fact that you guys assume spivak require no knowledge in proofs to do

can we start over

I need 2 books to do in parallel either calculus + proofs or calculus + linear algebra, introductory with no experience in proofs or calculus

[slender cargo]

Are you going to college or planning to? Are you interested in theoretical math or in computations/applications?

[gray gazelle]

theoreical/pure math

[slender cargo]

And will you be attending university?

Or are planning to?

[gray gazelle]

self study

[slender cargo]

I think reading a proofs book + Spivak's Calculus would be best

Linear Algebra can come later

[vital bane]

thomas' calculus for calculus and velleman for proofs

[vital bane]

then you can learn calculus + proofs + analysis from one single book "Understanding Analysis" by Stephen Abbott

not even kidding, it's so well written that you can actually do that

[tribal crow]

if you want smth for linear algebra, I'd recommend Friedberg, Insel, and Spence's book

a lot of people recommend Axler too

[vital bane]

Axler 4th edition is good

FIS is also good

[slender cargo]

imo going for Spivak immediately would be quickest

[vital bane]

spivak's calculus doesn't do metric topology, whereas Abbott does

[slender cargo]

Abbott spends like no time on stuff like integration by parts

[slender cargo]

Abbott spends only a bit on that

in the back

[vital bane]

no the entire chapter 3 is about that lol

[slender cargo]

I'm not sure if topology on the real line is a good reason to choose the book, but that's just me

[vital bane]

But I suppose you do need some calculus knowledge before doing Abbott

[gray gazelle]

I checked Thomas, it's 1.2k pages, compared to Spivak 650 pages? What is up with that?

[vital bane]

so i'd recommend this

[vital bane]

thomas has both mvc and single var calc that's why it's 1.2k

you can just use the first half of the book

[slender cargo]

Choosing between Thomas and Spivak should come down to if you want a more theoretical treatment or not

[gray gazelle]

Hmm but I need to do quiet a bit of a proofs book first before touching Spivak then?

[slender cargo]

No you don't. Spivak is an introduction to proofs as well, but it helps to have a proof book near you simultaneously.

[gray gazelle]

I do prefer more theoretical but I am not smart so I might be forced to use Thomas anyway

[slender cargo]

If you want to do proofs then imo you should choose to believe in yourself from the get go. You are smart enough.

[tribal crow]

in my experience, a proofs book is not as useful as just diving into the content you want to learn

you can pick up proofs writing skills along the way

[gray gazelle]

How is it an introduction to proofs? 5th exercise tells you to prove something without any assistance

[slender cargo]

You might have to spend more time in the initial chapters of Spivak if you're new to proofs, but that's fine

[gray gazelle]

Oh

[vital bane]

no Abbott is a much better introduction to proofs than spivak

[slender cargo]

That's fine. Just peek at the Answer Book if you need a hint. You'll get it eventually.

[vital bane]

it is literally written with the beginner in mind

[slender cargo]

So is Spivak

[vital bane]

I don't think so the differences are very obvious in the exercises

[gray gazelle]

Then I'm just learning to derive the answer, not proof?

[vital bane]

you can check for yourself

[tribal crow]

I mean at the end of the day, it's all somewhat the same; I'd suggest just choosing smth and going with it

[slender cargo]

I've checked out both. I think Spivak is appropriate

I could argue that Spivak is better as an intro since it goes through the field axioms rigorously, where as Abbott just says "assume what you know about R"

[gray gazelle]

lol

[slender cargo]

They're both fine but I like Spivak more if the person does not know any Calculus. Abbott does not go into integration by parts or any of that more computational stuff

[gray gazelle]

So in the end I should just use Khan Academy...

I'm joking btw

But this is getting messy again

[vital bane]

khan academy is what I used lol

[vital bane]

he does go into integration by parts

in the exercises

he introduces many things in the exercises

[slender cargo]

Like... barely. Yes lol

He assumes you already took Calculus

[gray gazelle]

The final verdict is: Spivak + Velleman/CZ -> Axler/FIS LA
or: Thomas -> Abbott RA + Axler/FIS LA?

[vital bane]

that's true

[vital bane]

thomas

[slender cargo]

I'm on the Spivak side

[vital bane]

you can also replace thomas with khan academy

since the ideas are what's necessary

you can later make it rigorous with Abbott

[vital bane]

he also introduces differentiation under the integral sign and fourier series and baire category theorem, like 4 different kinds of continuity, the henstock kurzweil integral, I'm telling you man this is a full on into analysis book (yes it assumes computational calc knowledge) but like it's so good!! it has so many good topics presented really well

[gray gazelle]

Do I roll a dice or...?

Actually

I will do first chapter of each and then decide

Is this a good strategy?

[vital bane]

good idea

[slender cargo]

Good strategy!

Keep in mind that with Spivak you get a two-in-one deal! You don't have to go through Thomas first

[slender cargo]

I mean, if I were arguing about what to use versus Abbott then I would argue for Bartle Sherbert or the other various Real Analysis books. To me Abbott is for a (slightly) different market than Spivak

[vital bane]

that's what I'm saying!

[fresh skiff]

I have already studied calculus. I am very much comfortable with derivates, limits and integration (for single variable). But I think there are some gaps, some stuff that I have missed. So i am thinking to study James Stewart calculus to fill those gaps. Then maybe I move to spivik or apostol.
(Currently on ch2 on Abbott).
Is this a good idea?

[graceful moon]

Eh I think if your calc is pretty solid and you’re doing analysis just move on, unless the gaps are major you’ll probably just pick up what you’re missing along the way

[gray gazelle]

What 2-in-1 deal?

[vital bane]

Just keep doing Abbott, if you have gaps just fill it with Khan academy

[gray gazelle]

And thank you guys for helping me!

[slender cargo]

Spivak teaches you the computational aspects of Calculus concurrently with Real Analysis.

The book was meant to be a first introduction to Calculus.

[vital bane]

but like it's more of a rigorous intro to calc than a full on analysis

spivak has a weird audience since it's not necessarily a normal calc book, but it's also not a full real anal book yk?

[slender cargo]

It covers the important parts of Abbott's book. The problems are as in-depth as Abbott's.

[vital bane]

I'm sure Spivak's problems are great

but Abbott's problems are more oriented towards theoretical aspects of analysis especially with the seqeunces, topology chapters

[tribal crow]

this is true, but I don't see it as a major issue

[vital bane]

not an issue, I'm just pointing it out

of course you can do like spivak + proofs then an analysis book

but I would just do calc then an full analysis book

[slender cargo]

The topology stuff is just recasting stuff about the real line. Bartle Sherbert doesn't do topology until the very end and it's still very much considered an Introductory Real Analysis book. You're going to learn Topology anyways in a separate course/book.

[tribal crow]

or, you can do what I'm trying to do

(Spivak's calculus book + FIS into CoM + ITM)

[graceful moon]

Yeah most UK unis don’t touch topology or metric spaces in their analysis courses

[tribal crow]

I didn't have any exposure to them either

[vital bane]

"The topology stuff is just recasting stuff about the real line"

untrue, metric topological notions on the real line (or R^n, metric spaces even) is an important aspect of real analysis, you see open sets, closed sets, clopen sets, compact sets, Heine borel theorem

several books have it

like Apostol, tao etc

[slender cargo]

Of course it's important for higher level analysis, but when trying to gain intuition at the introductory level, does it really lead to deeper intuition?

[vital bane]

ah when learning calculus? sure yea you don't

[slender cargo]

If you want to make this argument, you could say that they might as well go for Rudin! Just start with metric spaces from the get go.

[vital bane]

just change the metric from |x-y| to d(x, y) boom you have metric spaces most of the first half of analysis can be easily generalized to metric spaces if you work with topological notions such as open sets and compact sets (that's why they are important)

[marble solar]

Your comparison of the two is disingenous. You show the integrating factor method from Paul's Online Notes, but don't show the integrating factor method from Boyce & DiPrima. It's fine if you don't like Boyce & DiPrima, but I think this is more of an issue with reading comprehension skills rather than Boyce & DiPrima being poorly written

[royal remnant]

One gets to the point quicker, and one gets to the point slower

[marble solar]

I've used Boyce & DiPrima as my go to reference, and it's been a very clearly written text

[vital bane]

just to be clear I'm not disagreeing with you

[royal remnant]

If a book is bombing me with explanations instead of getting to the point, then I will never understand or remember what I am reading about.

[vital bane]

spivak is good

it just has a weird audience

[tribal crow]

fwiw, the audience exists

[marble solar]

Compare Paul's online Notes to this

[graceful moon]

To be fair I do also think Boyce is a bit wordy, but like the theorems and stuff are clearly seperated

[tribal crow]

the analysis course I took was meant for ppl going into math without any exposure to real abstraction, so to speak

because the hs curriculum here sucks

[marble solar]

The point was gotten too very quickly

[tribal crow]

but who still wanted to start off with "real math" ig

so Spivak is a good choice in this context imo

[marble solar]

Again, I think this is an issue with parsing information, you're not being "bombed" with useless information and "skipped steps". I think you're just having issues with reading a math book

[slender cargo]

I've looked at the problems from both Spivak and Abbott and Spivak's problems are on the same level (the theoretical ones, that is). If I had to ding Spivak on something, it's that there's a lot of exercises, so if time is limited and you are self-studying you have to be more selective which can be difficult.

[marble solar]

It's fine if you prefer Paul's Online Notes, it's a great resource. But eventually, you'll have to learn how to read

[tribal crow]

I'll admit that my analysis course is in a bit of a weird position though

[royal remnant]

Reading this part, I am like: "Wait, what the actual fuck. How did you get over there."

And in Paul's notes, the steps are detailed. It doesn't jump over things.

[tribal crow]

we also did a bunch of content not treated in Spivak in depth (e.g differentiable curves)

[royal remnant]

Like, how do they know if the integrating factor is e^(ax) something.

I need to refer back to the formula, and I couldn't find... a corrolation

u' = au

[graceful moon]

This is very much a you not knowing how to study maths from a book issue though, you just need to work through it

[marble solar]

Even paul's online notes skips this step

[royal remnant]

Nah? Is it really?

[marble solar]

Also the formula for the integrating factor is on the next page

[royal remnant]

Hold on, here

[graceful moon]

Boyce is also full of very clearly worked out examples after just about every new theorem or piece of information

[marble solar]

But that's not in the original screen shot

It even says "Without worrying about this magic $\mu(t)$

[hasty eagle]

MoonBears-C-

[royal remnant]

I thought, for some reason this was clear...

Unlike what was written in the other book

[marble solar]

You're literally cherry picking examples of what you don't understand, and then you don't even understand Paul's Online notes.

[royal remnant]

I am not cherry picking, I am showing where the problems accur

[marble solar]

It's literally the next page of Boyce & DiPrima

You can't be asked to read the next page?

[royal remnant]

Discouraged from reading when the introduction is crap

Pauls' notes did not have this effect on me

[marble solar]

That sounds more like a personal issue than Boyce & DiPrima being bad

Even your screenshots show that you didn't quite understand Paul's Online Notes

[royal remnant]

Once again, my method of learning is not reading walls of text. I would like illustrations and interactive learning.

[marble solar]

But you chose to read the walls of text instead of following where the equations are clear?

On the next page?

[tribal crow]

I mean, you can’t avoid this forever

[marble solar]

I get it reading is hard, but c'mon. You're taking a college/university level math class. At some point you have to learn how to read the texts

[tribal crow]

FIS has walls of text, but that doesn’t make it terribly written

it’s quite well written on the contrary

[graceful moon]

You started reading this stuff yesterday or the day before as well, it’s normal to be confused and not see the big picture yet

[royal remnant]

I don't think you quite understand my situation, which is fine. I don't even care, lmfao.

But the point is, when something is not properly explained to me clearly I can often panic and get dizzy

[graceful moon]

Also, as far as I remeber BDM has lots of pictures lol

[tribal crow]

that’s when you should pause and read again!

[graceful moon]

I have only read the back half of the book though

[royal remnant]

I did, I was like: What the fuck

[marble solar]

Then why study something that will make you panic & make you dizzy? Why even try?

[tribal crow]

read many times, think carefully about what’s going on

spend some time on it

[graceful moon]

Welcome to learning maths!

[royal remnant]

sigh

So I can't study anything, that's what you're implying?

Everything new, that isn't properly explained to me... will cause my brain to shut down

This isn't special to differential equations

[marble solar]

I'm not saying? You're the one that said it'll make you panic & dizzy

[graceful moon]

This is a you issue, and you’re just going to have to over come this at some point

Because you will hit walls when you’re learning new things

Maths would be easy if you could read a textbook like a novel and just get it

[royal remnant]

The reason why I study DE's and math is because it's interesting.

But I need to find a good study technique

and that's why finding specific resources is a good idea, tailored to my brain so it could comprehend it.

[graceful moon]

More reading, more problems less giving up when you hit a hurdle

[tribal crow]

this is very difficult to accommodate when recommending resources

we aren’t you, so it’s hard to help you find what you need

[royal remnant]

Yeah, but this is how I work

just saying, right

[tribal crow]

right

[remote vortex]

Yeah, if you genuinely get feelings of anxiety if the material isn't presented in a way you immediately understand, the best recommendation would be to get individual help.

A tutor and/or a therapist

I'm not saying that with malice, mental health issues are real and important to acknowledge and deal with

But discord isn't going to help with that

[royal remnant]

My reading comprehension is critically low. I always miss one tiny detail.
Always

Whenever I solve problems, sure, when reading short sentences on paper is fine. But, sometimes I missunderstand shit.

Because of memory related issues.

[royal remnant]

No it's just that my brain shuts down

more often

I get angry during courses, not at books online.

[slender cargo]

I'm going to concur with seeing a therapist. We all miss details and forget things.

I have to re-read a math page several times.

[royal remnant]

and then I turn to here to ask questions

Like I go to #❓how-to-get-help sometimes, if it's a specific thing

[slender cargo]

Keep flipping back to see what the definition says.

[royal remnant]

I'm genuielly suprised how I can solve DE's(not all of them) and be critically low in my reading comprehension.

[marble solar]

I guess the moral of the story is what happens when your go to golden source causes a panic attack? It's normal to be frustrated in math, and our emotions definitely shut down certain parts of our brain when we're heated. But it's something that'll have to be ironed out if not for your personal life, but for your professional life. Graduate school/Working environments are very intense

[royal remnant]

Panic attacks? Well, I don't feel like I have a panic attack. But I just go: "uhhh... what did I just read?"

[marble solar]

Referring to this point you made

[royal remnant]

Oh right, shit

[marble solar]

😄

[royal remnant]

Well, my teachers say that I am someone with huge intelligence and, have huge potential. But I have serious doubts about that too, my teachers, I feel like they are feeding me this superiority complex thing

(I'm not joking, I just... kinda wanted to share a little background)

[slender cargo]

Terence Tao talks about how complimenting someone "innate" intelligence can be bad. We get this illusion that it's innate intelligence that dictates whether or not you can do something, and not hard work.

Try to instead shift your viewpoint. It's hard work that you will get you places. And if others have succeeded, it's because they also worked hard.

[marble solar]

Moving to #math-discussion

[royal remnant]

Please, move this to #math-discussion

We can talk there

[violet shuttle]

When something feels like it is on the edge of making sense, like it's simple and I must understand but it is resisting attack like a buttery worm squirming out when you try to grab it, that will drive me crazy

I will obsess on it, etc. etc. insanity etc.

[tribal crow]

I don't really see another way to learn math lol

or physics either tbh

[violet shuttle]

well often it's not like that

it'll not make sense but it'll feel more like failing to grab a heavy object

as opposed to trying to grab ahold of something writhing out of your hand

it feels less annoying, less like you are on edge and just about to secure the worm

the worm thing doesn't happen too often

well i mean

okay it happens often

eventually i'll be able to walk away

the worm will of course still be in the corner of my vieion

and when i wish to try again with the full brunt of my wriggling, the worm is there

but then it is more controlled

does this analogy make any sense?

[tribal crow]

I'll admit, no lmao

but I kind of get what you're saying

Raine...

or... Sylvia now?

[opal spear]

this is something i face often too tbh, hi higher, yea

i got perma btw

[tribal crow]

I noticed

[violet shuttle]

hgmb?

as in, you relate?

[violet shuttle]

look man

I was partying friday

And then slept through Saturday

[opal spear]

yes! in fact the analogy is a pretty good description

[tribal crow]

this sounds so blunt coming from you lol

the worm thing makes sense

[tribal crow]

idk what you mean by this though

[violet shuttle]

Like ...

let's take a problem i had

perhaps det of exp of cartan?

[vital bane]

when something is on the edge of making sense I just try again tomorrow lol

tomorrow I think on why exactly it seemed to make sense

like taking a break from it always seems to help

[violet shuttle]

But like

I'm on the edge

I just have to

Like I have the problem loaded into my working memory

And it's almost done

[vital bane]

sometimes you have to take it out of the working memory for that sudden realization to hit you yk?

i think it's called diffuse thinking or something

[royal remnant]

uh

[violet shuttle]

This is true but it is not convincing to myself when obsessed

[royal remnant]

why are we having a discussion in book recommendations

xD

[violet shuttle]

I think of it like ambient thinking

[vital bane]

sometimes it do be like that

[vital bane]

right yea

[violet shuttle]

It does suggest books that are nonlinear

[royal remnant]

uh... what does? xD

[tribal crow]

this I can understand lol

[royal remnant]

like, what in particular

[tribal crow]

I give up sleep if it means I'll understand smth

[violet shuttle]

It suggests reading the chapter on root systems before that on how to get one from a lie algebra

[violet shuttle]

and it'll be very enjoyable

[tribal crow]

so real

[violet shuttle]

I'm not entirely my normal self right now

[royal remnant]

honestly, I study until I can't

xD

and, I might give up sleep at some points

[violet shuttle]

I'm nocturnal

Well I mean I just slept through yesterday

[royal remnant]

fricking vampire

[violet shuttle]

Except for the part where I woke up, was driven home, and then slep

[violet shuttle]

so truuuuu

[royal remnant]

xD

[vital bane]

I'm diurnal

[violet shuttle]

lamo

lamé be like

[vital bane]

I work throughout the day and sleep throughout the night, and I have no issues whatsoever

[violet shuttle]

#discussion

[remote sparrow]

@gray gazelle there are notes to supplement spivak. also, one can learn how to prove things by mimicking and adapting proofs given in the book. if you're very stuck, look at the solutions manual written by spivak.

[fresh skiff]

Understood thank you
Btw I was busy in university exams and some other stuff that's why I stopped to read Abbott for long time like a month today I started it and started by revision. All seems easy until I reach at particular theorem. Damn.. I end up looking at my notes to see how bla bla step follows

[vital bane]

I had the same problems

[vital bane]

where would the fun be if everything were easy?

[fresh skiff]

Oh.

[vital bane]

busy with (stupid) uni exams

[fresh skiff]

Same (exactly ). Well just 2 are left now

[fresh skiff]

Name of the author. In particular we are talking about the book
Understanding Analysis by Stephen Abbott

[tawny marlin]

what are some prerequisites before learning calculus? also, which book would y'all recommend to teach it step-by-step?

[remote sparrow]

solid background in algebra and trigonometry

[tawny marlin]

how solid? could i have an example?

[remote sparrow]

in stewart's calculus book, there's some diagnostic tests inside

if you find them difficult, maybe try brushing up on whatever skill is deficient

[tawny marlin]

ok thanks

[warped saffron]

I’m trying to learn abstract algebra anyone got any good books to buy?

[remote sparrow]

#book-recommendations message

[narrow relic]

I got a lot out of this book: https://centerofmath.com/textbooks/post/p_2398394
It's only $15.

[heady ember]

Look in pinned

[gray gazelle]

artin algebra
the harvard lectures on the book is also avilable on youtube

[silk sigil]

Is The Axiom of Choice by Jech comprehensible for someone who just finished an undergraduate program in mathematics, including one introductory logic course (which included basic discussion of ZFC and thus also AC)

And if it is comprehensible, is it recommended reading?

[inland hatch]

Does anyone know any lectures for graduate real analysis/analysis?

[gray gazelle]

There’s an ocw series for functional analysis

[inland hatch]

Anything that covers measure theory?

[raw jolt]

I'm trying to learn some cyrptography (I have basic intuitions and know several of the famous encryption techniques like RSA, vernam etc), what would be a good book to learn and cover these nicely and also learn a lot more indepth?

I would like to target this kinda stuff

rip i can't send images

[stark turret]

When someone tries to learn calculus without reading Kant and Hegel 🤣

[remote vortex]

Even the notion

[red night]

https://link.springer.com/book/10.1007/978-3-319-94818-8

[raw jolt]

can i send an image in dm? it's about the content i would like to see in the book

i want to know if its similar

[red night]

ye go ahead

[hearty steppe]

Anyone familiar with...

Kirillov A. An introduction to Lie groups and Lie algebras

or An Introduction to Groups, Groupoids and Their Representation by Ibort, Alberto; Rodriguez, Miguel ?

[hearty steppe]

also how do people feel about Topology - A Categorical Approach?

[violet shuttle]

Neither but I am familiar with Fulton and Harris's Representation Theory

[hearty steppe]

Was not a fan of that book

I've been trying to find a lie groups/lie algebras and representation theory text that isn't too heavy on the rigor

[naive veldt]

it seems to me that it is not, because this book is intended for those who are familiar with set theory at graduate level, but you can just try to start reading it, since the book is freely available online

[violet shuttle]

you... don't want rigor?

:c

[hearty steppe]

no I mean... I don't study mathematics like you guys and I don't have the best language comprehension skills in the world but theres certain books I am able to work through based on the wording of the exposition...

One particular challenging book that I enjoyed was Folland's Real analysis

[violet shuttle]

I don't understand

Perhaps you don't mean "rigor"

"rigor" refers to a specific thing that you certainly want

by language comprehension do you mean that the problem is that you are not the most comfortable with english?

[hearty steppe]

I'm not the most comfortable with a math book that doesn't really explain things with clarity in english... or there is no appreciative wording outside of proofs and formulas

I mean... one of my issues is I struggle a lot with reading comprehension

[violet shuttle]

fulton and harris have plenty of elaboration

[violet shuttle]

what do you mean by this?

[hearty steppe]

I get that a lot of people recommend that book, I just didn't like it

[violet shuttle]

That's fair

[hearty steppe]

it seems like... a good book for a mathematical physicist type of person and I hate those kind of books generally

[violet shuttle]

Lol when I described how I read it to someone here he's like "Yeah, but that's why it's not a good book, even if you can teach yourself well from it"

[violet shuttle]

wdym?

i don't understand

[hearty steppe]

like every mathematical physics book I've read so far I don't like... for instance Brian C Hall expository flavor texts

[violet shuttle]

it is indeed true that i plan on going into physics and not math but that makes me less likely to read fulton and harris

[violet shuttle]

oh so you want less exposition?

[hearty steppe]

less overly formal exposition*

[violet shuttle]

what does that mean??

[hearty steppe]

cuz I struggle with too much formality

[violet shuttle]

what do you mean by formality here

if you want something that's...very dense... Humphrey's is a choice

I strongly don't recommend it

[hearty steppe]

So what I like about Folland is even though there is a lot of formality, there is a lot of general points of clarity brought into the picture

[violet shuttle]

I don't understand what you mean by formality here

[hearty steppe]

ugh I will be forever waiting for a representation theory and lie theory book I'll be able to work through nevermind lol

ok well a book I'm enjoying right now is Probability and Measure by Billingsley... For some reason the delivery feels just right

[opal spear]

What are some good books for diff geo?

hi hgr, why

[tribal crow]

thinking, of course.

I obviously haven't done any DG yet, but I've been recommended Lee's ISM, Tu's manifolds, and do Carmo's diff/riemannian geo before

Spivak also has a multivolume series

[opal spear]

ah, thanks for the recomm! im stockpiling on books because... i don't know but it's kinda like an itch

[tribal crow]

I have over 30 DG book pdfs in a folder lol

I get what you mean

@opal spear maybe this is useful?
https://math.stackexchange.com/questions/13575/teaching-myself-differential-topology-and-differential-geometry

it's kind of a lot of recommendations though

[opal spear]

thanks!

[hearty steppe]

the introduction to groups book looks like a good read for me after skimming through it

[opal spear]

yea, ill try to go through them and see if anything sticks
also, is CoM diff geo?

[tribal crow]

I've been told to go through CoM before attempting DG proper

I think it's a lot of multivariate analysis, and then some basic notions of DG towards the second half

[opal spear]

gotcha

[prisma relic]

Not anymore cuh. You fell off 😦

[slender cargo]

I'm gonna check out Harold Edwards Advanced Calculus: A Differential Forms Approach. It looks like a fun book and Axler of LADR fame thinks highly of it. He has complete solutions in the back of the book!

[mossy flume]

https://ncatlab.org/nlab/show/carrying

[marsh ingot]

Wha?

[trail hemlock]

i miss whem my math books had animals on the front

now all i see is "international series in pure and applied mathematics"

v

[abstract copper]

Read Axler if you want cat surprises

[violet shuttle]

arnold

full of cats

numerical symplectic integrators are an excuse to look at cats

[abstract copper]

Griffiths qm has a cat as a cover. Too bad it's not really good

[sage basin]

if I ever have enough clout to write a book I will put something cute on it like an animol

[hallow oriole]

i have faith

[fervent marten]

any free pdfs for intermediate/advanced algebra problems?

[violet shuttle]

This server does not allow discussion of piracy. I will point out that piracy exists.

Anyways, I have my physical copy of Lang's Algebra which I like

[molten mason]

I'm waiting for another big sale to get mine. I'm tired of squinting at my screen

[narrow relic]

Have you seen his Linear Algebra book?

[violet shuttle]

he has an undergrad curriculum

[narrow relic]

Is that a question?

[tribal crow]

it’s the truth.

[narrow relic]

Indeed it is!

But I was trying to understand Xela's answer to my question.

[tribal crow]

she knows about Lang’s books haha

[narrow relic]

I was trying to ask "if you have seen Lang's Linear Algebra book, what is your opinion of it?"

[tribal crow]

I see

[violet shuttle]

I haven't read a word of it

Given that his Algebra book is the famous one

It seems that the others weren't as good

[narrow relic]

OK! Thanks.

[molten mason]

I can't remember off the top of my head and I don't have much to compare it to, but I enjoyed it

[narrow relic]

Cool, I have been enjoying it as well.
The only "downside" I've hit so far is that he doesn't have quotient spaces.

[remote sparrow]

have you tried using the coupon codes 50OFF and HLT23 on springer?

alternatively, get a used copy and gamble on the fact that its binding may be better than a new copy

[narrow relic]

Hi Sour Drop! 🙂

[narrow relic]

Thanks for sharing these; I just tried them but it said they were expired.

[remote sparrow]

well i guess they fixed them

[narrow relic]

I sometimes worry some of the older books will go out of print and I'll never get a chance to get a copy.

E.g. that Lang Linear Algebra book is from 1987.

[fervent marten]

oh cuz like a few months ago i got a decent legit pdf from someone

[ripe panther]

math book is good

[rigid forge]

So uhm, I kind of spent all my time on math and haven't done any physics this year. does anyone a short book/lectures/notes that explain basic concepts(magnets, electricity, light, gravity, all that stuff) in a concise way?

I have about a week or so

[eager sandal]

Check out Feynman lectures notes website but I don't think anything would be as tailored for your exams as the lecture notes provided by your lecturers.

[rigid forge]

will check them out

[lusty ermine]

which references are good for exercising recurrence relations

[abstract copper]

Griffiths E&M is your best bet, but it's not short. It's often regarded as the best undergrad EM text

[viscid comet]

I want to find some introductory physics texts but I don't want some Burbaki shit

I've been reading very mathy novels and because it isn't nearly as exhausting as some of my more burbaki-esque books I feel like

My math knowledge is some multivariate calc and some diffeq

[remote sparrow]

https://www.amazon.com/University-Physics-Modern-15th/dp/0135159555

you can get an old edition to save money

most introductory calc-based physics books are pretty similar

[viscid comet]

Hmmm

Cool

[abstract copper]

Do you want an in depth to a particular subject or just an introduction to a broad varieties of subjects?

[viscid comet]

I have a particular interest in thermodynamics and classical mechanics (pretty disparate fields but shhh)

[abstract copper]

For classical mechanics, Taylor's introduction to mechanics is good but very lengthy, and for stat mech, I'm not really sure.

[viscid comet]

Any suggestions for thermodynamics if I decide to pursue that?

[abstract copper]

I don't know, haven't really studied it myself. But I see people recommending Schroeder's Thermal Physics.

Should try asking the physics server

[viscid comet]

True

Talked to the (stinky) physicsts

[gray gazelle]

Goldstein's classical mechanics?

i think its a pretty standard choice

[abstract copper]

Goldstein is intended towards grad students in physics which isn't a good intro.

[tribal crow]

but the OP has everything they need to start reading Goldstein, do they not?

multivariable calculus + differential equations is typically enough to start most classical mechanics books

[gray gazelle]

hmm i used it in an undergrad class

[tribal crow]

it's used in UG classes a lot

Goldstein, Taylor, and L&L seem to be the common ones from what I've seen

[gray gazelle]

but i guess it would be hard to start from if you haven't at least seen some elementary kinematics/dynamics

[abstract copper]

Must have gotten confused with some other texts. Just looked up Goldstein and yup you're right. My bad.

[gray gazelle]

cause it goes straight into lagrangian mechanics

[violet shuttle]

I fucking love Goldstein

[violet shuttle]

As you should

I learnt what a lagrangian was before I learnt what an integral was

and this is fine and dandy

[tribal crow]

Xela, thoughts on L&L's Mechanics?

[violet shuttle]

Haven't read it. Probably good

[tribal crow]

fair enough

I'll probably either read it, or Goldstein when the time comes

[abstract copper]

L&L is good.

Currently using it

[tribal crow]

I haven't really taken a look at it too deeply, could you give me some thoughts?

[abstract copper]

Doesn't skip much math, it starts from the beginning like what inertial frames of reference are, explained what the Lagrangian is (quite detailed). It's 186 pages but covers about pretty much the same stuff as Goldstein. The downsides are the lack of exercises and each exercises has an answer directly below.

[tribal crow]

I see

thank you for your input, I appreciate it!

[cobalt badger]

Holy shit, unfathomably based

I’ve also been contemplating whether to read something like Taylor first, or jump straight into Goldstein, once I get the requisite math background

[violet shuttle]

I have Taylor for a class rn

imo...me no likey

Half of this class is what I believe is taught in an undergrad diffyq class

And likewise this is substantial portion of taylor

e.g. paul's online math notes on the damped driven harmonic oscillator has more fucking depth

[tribal crow]

I haven’t heard amazing things about Taylor in general

[cobalt badger]

I see I see

[tribal crow]

a lot of people seem to find it horribly dry I hear

[cobalt badger]

hmm

probably will start straight with goldstein someday

[tribal crow]

L&L is tempting to me because it’s short

I have a strange tendency to prefer shorter books for some reason (CoM, L&L)

[gray gazelle]

goldstein is horribly dry as well

[cobalt badger]

i kinda wanted to skip the “introductory physics” textbooks (Young and Friedman types, Stewart Calc equivalent of physics essentially), by first acquiring all of undergraduate math in math textbooks, so that I could skip all the mechanical calculations with numbers and units and stuff
wasn’t sure if that was a good idea, but maybe i’ll give it a shot and jump straight into goldstein, shankar, jackson, by learning all the math first

[tribal crow]

do it

the intro physics textbooks are so boring

it’s unbelievable

[cobalt badger]

ifkr

[tribal crow]

I guess it’s not all bad though, because they’ve driven be towards the direction of math

[cobalt badger]

i tried to do the chapters on vector in Young and Friedman (touching it 3-4 years after high school)…it was so incredibly boring but i convinced myself it was a necessary evil to get that foundation.

[tribal crow]

I’m gonna guess that my interest in physics will pick up once more after I get exposure to non intro stuff

[cobalt badger]

Left it after like question 70 or 80 of the exercises. EVERY question had numbers like 30.74 m or 57.21 N

couldn’t stand it

[cobalt badger]

based

[tribal crow]

I think it was a good choice

me no likey annoying numbers either

[cobalt badger]

yeah same. i remember doing some of the more symbolic derivations from high school, and some of those were so fun, even with just basic calculus usage

[tribal crow]

that kind of stuff is the only redeeming aspect of intro physics lol

[split bluff]

just guess the solution if it demands a number bro

ez

[remote sparrow]

numbers are good in intro physics

you should be able to know the rough size of your answers

[cobalt badger]

I keep looking at Griffiths E&M every now and then (for some reason I love to flip through pages of unfamiliar material), and some of the stuff looks super beautiful

[split bluff]

ngl physics looks cool when one looks at solutions from some book

one of these days i may grab a physics book and read some of it

[gray gazelle]

why would you do that to yourself

[split bluff]

for fun bro

i do math for fun, may as well do some physics, i don't know

though these days it's been hard, i've been doing combinatorics and it's kinda hard

didn't know counting was so hard 😔

[heady ember]

Infintary combinatorics in the corner: Hehe boi

[split bluff]

well i took an algebra course even thought i study computer science and it's been good so far until they made me do combinatorics which i only knew superficially, i've been reading combi stuff here and there and look at proofs for some problems ans stuff

i lurked this section the other day and someone recommended bona's combi book but after reviewing it i noticed i had some knowledge gaps that i'm trying to fill with some other easy book i found the other day

[opal spear]

do it frfr

[violet shuttle]

wdym

goldstein is fun

shankar is fun

wald is fun but dense and christ please don't try to learn dg+rg from him

[thorn birch]

Hey please anyone suggest me a good book for euclidean geometry?

[opal spear]

elements by euclid

[violet shuttle]

except he fucks up pretty early on

and what's this shit with these axioms

there's Hilbert or something

i still don't know a proof of the pythagorean theorem

[scarlet steeple]

still great book to read imo

I read this translation probably also abridged and it was fun

yes it may not be as rigourous as we're used to but you'll defintely learn some geometry

and history ig

[jaunty acorn]

need recommendation for a beginner friendly book on logic and set theory

[glass kernel]

Hey all ok am a first year student at uni and having this exam for discrete maths and maths 1
But the thing is I haven’t practiced at all
So do you guys know any specific book for this 2 subjects from which I can practice a lot of questions

[fervent marten]

https://tenor.com/view/imaneedthatchicken-credit-card-credit-card-slam-gif-23658780

[covert mauve]

oopsie

wrong server

[gray gazelle]

https://quomodocumque.wordpress.com/2013/01/29/katos-lecture-notes-are-like-a-modernist-novel-about-commutative-algebra/

[gray gazelle]

Whats the latest edition of Thomas' Calculus?

[wet sentinel]

any recommendations for good elementary number theory books

[narrow prairie]

niven

[wet sentinel]

what about zuckerman

[lusty ermine]

which book has hard real analysis exercises, computational

[fresh skiff]

Paugh, rudin, amann?

[wet sentinel]

wdym by computational

this will be calculus instead

[lusty ermine]

non proof

[wet sentinel]

analysis is just proofs

[lusty ermine]

okay

calculus then

[wet sentinel]

so you want to compute derivatives limits integrals etc ?

[lusty ermine]

yes but special limits special integrals

do you know any book like that for caclulus?

[wet sentinel]

so what is meant by special

[lusty ermine]

for example one common thing I have seen in limits to avoid differentiation is rationalisation, division and multiplication by the conjugate

is there any other things like that for calculus

if possible that it includes how to integrate inverse trigonometric functions, or hiperbolic functions

also, any references for hard trigonometry exercises?

[tribal crow]

I was referring to these types of books, not Goldstein, Shankar, Wald, etc lol
#book-recommendations message

[violet shuttle]

I've never heard of those

[tribal crow]

because you skipped all of them! (which is the correct way by far)

[slender cargo]

Try Calculus by Michael Spivak. He has harder computational problems.

[remote sparrow]

#book-recommendations message

#book-recommendations message

[remote sparrow]

#book-recommendations message

[primal terrace]

i want to get good at math (currently doing As level aka grade 11 math)

i dont know what books i should do to improve

[rigid forge]

not really book releated, but what do you all use for taking notes? I use paper till now, but not having the ability to erase and writing being considerably slower is a bummer.

[lusty ermine]

mechanical pencil + eraser does not work?

[rigid forge]

I prefer writing with a pen on paper

[glad rampart]

I’ve never taken notes

[violet shuttle]

I find it useful

The note taking helps me learn the content, even if I don't look back

and when it comes to presenting to someone else, the note taking is helpful

[glad rampart]

True

Probably will more in the geometry book since there’s more formulae to use

[echo tendon]

https://www.alibris.com/Hands-On-Machine-Learning-with-Scikit-Learn-Keras-and-TensorFlow-3e-Concepts-Tools-and-Techniques-to-Build-Intelligent-Systems-Aurelien-Geron/book/51760265?matches=17

is this valid?

I need to learn ML/DS

I found a pdf of it online and the intro chapter is pretty good

[split bluff]

i don't know man i don't do notes really but if i had i'd use latex

i just do enough exercises for some subject and theorems get burned into my brain and i hardly forget about them

[fresh skiff]

Why not using the $\LaTeX$?

[echo tendon]

I dont really take notes in general but when I do want to put my ideas together for reference I use latex

[foggy relic]

whats a good book for abstract harmonic analysis, with rep theory & number theory in mind

i only know folland

[wet sentinel]

which one do you prefer

[sage python]

Deitmar Echterhoff is good

[remote sparrow]

burton

[wet sentinel]

what is special about it

[remote sparrow]

it's very straightforward, no curveballs

[wet sentinel]

ohh ok tysm

does it have solution of exercises

and what is the level of exercises

[remote sparrow]

i think there are some answers in the back

not 100% sure

[remote sparrow]

easy to moderately difficult for the most part

[wet sentinel]

ohh ok tysm

[wet sentinel]

is there somewhere that has some difficult problems if i want to check some from time to time

[remote sparrow]

niven, zuckerman, and montgomery

[wet sentinel]

sorry if i am bothering you with my questions but are there solution manuals or somewhere that has solutions to the problems of these

[remote sparrow]

i think there might be hints in the back

i don't know of a solutions manual

[wet sentinel]

ok tysm

[hallow oriole]

niven has an intro nt book that isn't related to int or tnt?

interesting

[remote sparrow]

what are int and tnt

[hallow oriole]

irrational and transcendental number theory

[remote sparrow]

https://www.amazon.com/Introduction-Theory-Numbers-Ivan-Niven/dp/0471625469

[hallow oriole]

neat!

[foggy relic]

langlands arc

?!?!

ok wait is the first book a prereq for this daminark

'A first course in harmonic analysis'

"principles of harmonic analysis"

or can i go straight to book 2

[sage python]

I don't think one of them is a successor to the other?

[foggy relic]

based

how much measure theory do you thing is a prereq for abs harmonic analysis in general

whether this book or follands

i know just the basics, like sigma algebras, outer measure, lebesgue stuff

[sage python]

You should know most of a standard measure theory class

L^p spaces, Riesz representation theorem

[foggy relic]

ohk nice

[heady ember]

I think Richard Borcheds recently made a video on the Selberg Trace Formula. Perhaps you'll be interested in taking a look.

[crimson leaf]

The authors mention this in the preface

[sturdy shore]

I read the first 3 chapters of that book, the only time it refers to the other book is when stating what the dual groups of R and S^1 are

from what I recall at least

[gray gazelle]

I wanted your opinions on the order I should start these books:
1-Introductory Mathematical analysis ( real analysis ) - WITOLD A.J. KOSMALA
2-Vector Calculus By Jerrold E.marsden
3- Contemporary Abstract Algebra by Joseph A. Gallian
4- Numerical Analysis By Richard L. Burden
5- Differential Equations by Kurt Bryan

here is my background
1- Year of calculus, Done up to multivariable chain rule, double integrals and triple integrals and directional derivatives
2- Linear Algebra

[tribal crow]

what are your goals?

[gray gazelle]

I know at some point I want to study number theory algebraic or analytical

but I am picking up the required knowledge

my professor gave me the book above before retirement as he knows that I am planning on doing real analysis , complex and abstract algebra

[tribal crow]

in that case, I'd probably say that real/complex analysis and abstract algebra would be the most important topics you hit up

[gray gazelle]

and multivariable and diff eq and numerical analysis ( not related to me wanting to study advanced number theory )

[gray gazelle]

which do u recommend

first

abstract or real

[tribal crow]

that would depend on whether or not you prefer analytic or algebraic number theory haha

[gray gazelle]

I still feel I am developing my math maturity

[tribal crow]

there's also the possibility that you do both books simultaneously

[gray gazelle]

I didn't take any number theory course yet

lmfao

[tribal crow]

which I think it possible too

[gray gazelle]

so I don't know tbh

But even if I ended up not doing any of these

I would still do these courses I guess

the question is which order do

[tribal crow]

to be honest, I'm in no position to tell you which topic you should do first

I myself don't know any number theory lol

[gray gazelle]

hmm , the question is

which will help me more develop math maturity

[tribal crow]

real/complex analysis and abstract algebra just tend to form a solid foundation for the rest of math

so I suggest doing those first

which of the two should you do first? I haven't the faintest idea lmao

I think either or would be fine, or both at once

[gray gazelle]

which do you think would be easier on someone who didn't pickup math maturity from lin alg

I didn't have much time for this course which made me not study it much

I feel abstract would be harder on me since it would use a lot of concepts developed from lin alg

correct me if I am wrong

[tribal crow]

to the best of my understanding, abstract algebra tends to be fairly disjoint from linear algebra, actually

linear algebra isn't too present in group theory, afaik

[gray gazelle]

fr?

[tribal crow]

in ring theory it's there, though it's nothing too different from what you already know

[remote vortex]

Yeah, I wouldn't say linear algebra helps very much in abstract algebra.

[round shore]

Hm, commutative algebra or representation theory is full of lin alg

[tribal crow]

of course, but DoubleW is reading Gallian, which doesn't cover either topic

[gray gazelle]

hmm , then I guess it is put as a prerequisite in my college curriculum just for the sake of testing students' math maturity since lin alg is the very first different from calculas as it can require some proof

[gray gazelle]

yep , I don't think it is there

oh there is a section called

vector spaces

linear alg alert

[remote vortex]

Linear algebra is also more generally useful, so it makes sense to put it earlier in the curriculum.

[round shore]

What kind of algebra does it cover if there is no comm alg?

[tribal crow]

basic groups, rings, fields stuff

[gray gazelle]

I think only chapter 19 , vector spaces

[tribal crow]

Gallian is known to be a very light introduction to AA

[gray gazelle]

is the one requiring lin alg

as far as I am concerned

[tribal crow]

this is still my final verdict

it really does depend on you

[gray gazelle]

the thing is that

I only did calc 2 as self study

other courses all are instructor based

I wanted to do a more rigourous topic as a self study this summer

[hallow oriole]

if ur still developing im gonna say analysis

subjective but nothing else gets into the nitty gritty quite like anal

[tribal crow]

I disagree, but I was trying to be as unbiased as possible

[gray gazelle]

elaborate

why do u disagree?

[tribal crow]

personal reasons

[hallow oriole]

actually yeah why do u disagree? i wanna hear alternative opinions

hgrrrrrrr

[gray gazelle]

I am open to opinions

the thing is that

For real analysis , I don't know if I am ever gonna do it here in my college

[hallow oriole]

are you doing a math major

[tribal crow]

it's probably a serious skill issue on my end, but I found analysis to be much more frustrating and opaque lol

[gray gazelle]

the prof currently doing it is known to be very hard

[hallow oriole]

ohh yeah im not denying that

[tribal crow]

I almost quit math entirely because of it

[gray gazelle]

Yesssss

[tribal crow]

LA kept me from leaving entirely lmfao

[gray gazelle]

I am quitting CS because of data structures

hehe

[hallow oriole]

i think that if ur gonna be doing analytic number theory you'll need to be lovers with frustration and opaqueness

[tribal crow]

I don't deny that RA is really good for developing math maturity, but it can also be super painful

[hallow oriole]

then there's almost a 100% chance you'll have to do real analysis 😭

[tribal crow]

they said they might do either analytic or algebraic

[gray gazelle]

I know right

[hallow oriole]

ohh or

hmm

[gray gazelle]

But I don't think next year

[hallow oriole]

i guess it's dependent on what kind of nt you like atm

[tribal crow]

in any case, math majors must do RA and AA anyways

[gray gazelle]

well , it is elective for pure math students in my college

[tribal crow]

the choice is yours on which to do first

[gray gazelle]

I think I will do AA

[hallow oriole]

whoa, real analysis isnt required?

[gray gazelle]

Pure math students get to choose between RA and topology

[hallow oriole]

huh

interesting

[gray gazelle]

the thing is

I am computational math major atm

[tribal crow]

that seems like a very stupid choice

[gray gazelle]

might change it

[tribal crow]

they should do both lol

[gray gazelle]

Tbh , If I am gonna be a pure math major

I am gonna do only RA

I don't think topology is useful for me

[round shore]

Only real analysis without topology?

[gray gazelle]

yes

[tribal crow]

idk how it is elsewhere, but the applied math people at my instituion are forced to take RA, AA, topology, PDEs, diff geo, etc

[gray gazelle]

topology is a hard topic that doesn't align with my interest

[tribal crow]

maybe that's overkill though

[gray gazelle]

my college isn't that great

last time PDE was offered

[round shore]

You won't go very far in RA without topology lol

[gray gazelle]

was 3 years ago

or 4

[hallow oriole]

there's a lot of topology in number theory

[round shore]

In all maths tbf

[gray gazelle]

oh no

[tribal crow]

all of maths shows up in all of maths

[gray gazelle]

welp

[tribal crow]

it's all useful in the end

[gray gazelle]

now I'mma focus on computational side of math

[hallow oriole]

it doesn't really matter what you do (analytic or algebraic) you'll see a large amount of topology

[tribal crow]

to varying degrees, but useful nonetheless

[round shore]

But you can't do ra without topology

[gray gazelle]

I have never seen topology as a prequiste anywhere for that

[tribal crow]

@gray gazelle I also don't see a reason why you can't self-study topology, or anything else you may need for AnaNT/AlgNT

[hallow oriole]

it's not a prerequisite

[gray gazelle]

HA????

how

[hallow oriole]

you'll just see it everywhere

[tribal crow]

you can self-study anything you're missing

[gray gazelle]

that is what I like about math maturity

but at the moment , I am trying to self study subjects so I know what subjects I will do in college so when I do grad school , I have good courses on my transcript that can support my application

[round shore]

Most of properties of R comes from connectedness,completeness, compactness. Everything involving continuity and limits is topology

[tribal crow]

I believe that the development of topology was historically motivated by real analysis, actually

[hallow oriole]

the modern treatment is necessarily different from the historical treatment tho

[gray gazelle]

but I ain't required to do a full topology course or a self study a book to study RA , right?

[tribal crow]

my point wasn't about the treatment of topology, but rather the usefulness of topology in RA

[hallow oriole]

oh, sure

fair!

you'll need topology to do research in ana/algnt tho

im not an expert but it has to be true

[tribal crow]

I'm starting topology in a week or so, let's pray for me

[hallow oriole]

LMAO u got this

[tribal crow]

thank you

[gray gazelle]

Good luck with that
u got it

my problem with topology and my problem with Physics that I decided not to do it

is imagination

I don't have a great Imagination ability

[round shore]

To learn the very basics of real analysis? No, you can prove the results "by hand" (it'd still be topology,but kinda hidden if you want), but that works for like the first year only

[gray gazelle]

I really relied on following examples

[gray gazelle]

oh

[tribal crow]

I have terrible imagination too

it's still possible to learn it well

[gray gazelle]

so If I were to do more Real Analysis

hmm

and that would be required for number theory ?

[round shore]

If you want to do maths past the first year tbf

Yes

[tribal crow]

when we spoke of any sort of geometry in LA, I was always unable to imagine it well

needed animations or smth

[gray gazelle]

dang

[tribal crow]

but LA is still my favourite subject

[round shore]

If there is 2 things you can't avoid, it's topology and Lin algebra

Since they're in all areas of maths

Unavoidable

[hallow oriole]

i think you'll find you don't hate it as much once you become more mathematically mature

[tribal crow]

this.

I hated RA beyond belief ~7 months ago

now that I'm wiser, it's not so bad

[gray gazelle]

done one

1 to go

okay

[tribal crow]

in retrospect, it was very valuable

[gray gazelle]

I hate imagination

[round shore]

Yeah. Maybe you'll still hate purely topological arguments, it happens, but the language will and should become natural

[hallow oriole]

that's okay, imagination is a learnable skill

[gray gazelle]

I have always said that my math maturity started when I dropped phy major because of my weak imagination ability

[hallow oriole]

me with elementary set theory (the unironic most torrid awful field of math)

[gray gazelle]

doubt it

I did poorly in data structure

[hallow oriole]

i am so so grateful that none of the advanced classes include intro set theory things

[gray gazelle]

when it came to simple trees and graphs

[hallow oriole]

the past does not determine the future

[round shore]

Maybe you just don't think about it anymore lol

[hallow oriole]

ill count internalizing my worst enemy as defeating it

[gray gazelle]

imagination is my own enemy

fr fr

[hallow oriole]

it's learnable!!

i solemnly swear

[gray gazelle]

I never managed to learn it

I just ended up looking at examples

and following them

[gray gazelle]

maybe it is for someone with an actual talent

[round shore]

No

Don't think too much about it

[tribal crow]

you'd be surprised.

[gray gazelle]

that I don't have a talent

[tribal crow]

there comes a point where you have a sort of intuition for these things

[gray gazelle]

yes I were suprised

I came to us with the intention of doing cs and phy

here I am looking at grad school for math

[round shore]

Fortunately you don't need talent to do maths

[gray gazelle]

lmfao

[gray gazelle]

yep that is it

[tribal crow]

it came as a shock for me to find out that I had developed an intuition for linear algebra, despite having a terrible time with imagining things in said subject

it'll come for you too

I promise

[round shore]

He's right

[gray gazelle]

I am believing u from personal experience with lin alg too

[hallow oriole]

even if you don't end up developing intuition for it, struggling through it will be a valuable experience iaoi

[gray gazelle]

me with series :

[tribal crow]

bashing your head against the (metaphorical) wall is a stupidly powerful way to learn maths, I found

[gray gazelle]

why metaphorically ?

[tribal crow]

I'd hope you're not incurring any concussions by using a real wall

[gray gazelle]

It helps ngl

[tribal crow]

metaphorical wall = some stupid problem/theorem/proof you've been stuck on for 100000000000 years it seems

[hallow oriole]

i find taking a walk is a significantly better way to outlet frustration

[tribal crow]

sometimes even examples can take a long time to understand

[round shore]

I believe hitting your head against a wall is bad for your (maths) abilities.

[gray gazelle]

it is actually good

[hallow oriole]

perhaps a quick nap

[gray gazelle]

it lights up the lamb up my head

[round shore]

It destroys brain cells tho

[hallow oriole]

i dont actually know if ur being serious or not but please don't hit ur head into walls

that's how people die

[remote sparrow]

have you tried abusing antidepressants and amphetamines? it worked for erdos

[gray gazelle]

im kidding

[gray gazelle]

done

[hallow oriole]

omw to follow in the footsteps of my fellow adhd king

[tribal crow]

I would not recommend drug abuse

[hallow oriole]

or at least i would be if adhd meds did jack shit

BUT when i get my shit tgt it's over for yall

[gray gazelle]

I used to use modafinil

but that is about it

[tribal crow]

it's been over for me since I decided to study maths at all

[hallow oriole]

do a cs major on the side it's like five extra classes

[gray gazelle]

only a minor

[hallow oriole]

and you get employed when you finish college

[gray gazelle]

doubt it

[tribal crow]

cs majors are a lot more than 5 extra classes here

[humble creek]

any first book for functional analysis that also covers necssary measure theory?

[tribal crow]

Folland

[hallow oriole]

oof

[tribal crow]

I suppose this book is more measure theory than functional analysis, but it covers both

[hallow oriole]

probably still worth taking a few cs classes on the side then

[tribal crow]

I have a couple of DSA courses in mind, perhaps a couple of stats courses too

[gray gazelle]

so as a final decision between

RA and AA

[tribal crow]

though I might replace the stats probability course with an actual probability theory course lol

[hallow oriole]

for the record there's no need to do a final decision

[gray gazelle]

should I go for AA?

[tribal crow]

it's totally up to you; I would personally say "do both simulatenously, and perhaps drop whichever one you like less"

[hallow oriole]

u can just do both

[tribal crow]

you don't have to drop either, but if one of them is more enjoyable for you, focus on that one

[gray gazelle]

If I am free

I would do both

[round shore]

Both

[gray gazelle]

but I am having a math internship on dispersive equations

which would require me to do some vector calc I guess

so I know I would do some vector calculas and something else

hmm

[tribal crow]

if it's utterly impossible for you to decide, I suggest flipping a coin

[gray gazelle]

I think I will go with RA since it is related to calc

btw

how good these books , I got them for free but I don't know if they are good enough

[hallow oriole]

they're fine

[remote sparrow]

your wallet will not last long

[gray gazelle]

well

I can sell the bad ones

And buy other good ones

or use the library