/sci/ - Science & Math

I am studying linear algebra

>>9148411
organic chemistry

Physics. I'm glad there is always /mg/ where I can share my physical intuition, reddit is great too though.

Just gotten into the high-tier shit my dude. Rational numbers. Good shit.

Japanese animation.

How importand is calculus in AI research?

Or should I focus my attention mostly to statistic and linear algebra?

>>9148482
>How importand is calculus in AI research?
Extremely.

>Or should I focus my attention mostly to statistic and linear algebra?
No. Study all the calculus you can get your hands on.

Can someone point me to some cool results which I should be looking forward in Papa Rudin? I'm finishing his first chapter (so definitions of measures/integration).

I've always found it difficult to motivate myself for analysis, in topology and algebra there are always some problems out of my reach proof wise but which are clearly interesting.

why isn't math open-sourced lads?
so you can get a job?

>>9148493
can a function be defined to have two unique derivatives?

>>9148470
every day i wish im in math instead of compsci

I want an archive of all these anime math nerds with textbooks pls

>>9148660
same

What background knowledge should I have for studying something like information theory?

>>9148738
Anabelian Geometry, Probability Theory, Arithmetic Elliptic Curves in General Position, The Galois-Theoretic Kodaira-Spencer Morphism of an Elliptic Curve

How the fuck do I into discrete math

>>9148440

>>9148755
what are you having problem with lad?

>becoming extremely proficient at chain rule derivatives
Goddamn I feel like a wizard.

>>9148754
epic

>>9148571
But it is, it's called libgen.

>>9148765
Understanding an Indian professor trying to explain propositional logic. I can understand the lectures and in class assignments but the homework she assigns is fucking miserable

>>9148411
Reading through this. Pretty good so far.

just started combinatorics
wish me luck sci

>>9148838
oh god

>>9148866
Didn't expect much from Tao, but i now prefer it to Zorich.

>>9148411

>>9148576
WTF ? Partial derivative with different derivation variable could I that but I'm pretty sure you weren't thinking about this.

>>9148509
here are a few:
Stone-Weierstrass theorem
Radon-Nikodym theorem (though it might not be immediately obvious why it's interesting)
Fourier inversion formula
Riesz representation theorem
Riemann mapping theorem

What are some good books on maths? Not books about teaching math but I guess the more philosophical thoughts behind it, books that are more motivational and inspirational instead of about teaching math

>>9149083
Riesz and Radon seem particularly interesting. Stone-Weierstrass was in PoMA and is quite good. If I'm not mistaken Riemann's can be used to prove the Jordan Curve Theorem very quickly too. Thanks anon.

>>9148838
Is this Tao's book? Title please.

>>9148847
>Indian
>she
Diversity is so beautiful

Systems of differential equations for the second time this year.

/brainlet/ here

>>9149712
stay strong anon. i got a B in multivariate calc in undergrad, but aced multivariate analysis in grad school. sometimes it just a matter of time

>>9148426
Nice

>>9148411
supernatal activities at midnight and frankly they don't scare me like other people.

>mfw Trying to understand Ordinal Collapsing functions, Proof-theoretic Ordinals, and all the other ordinal nonsense

What the fuck is this shit

>>9149186
Analysis 2, 2nd edition hardcover. Cheap, but amazing book.

Is self-teaching viable in math or do you need a tutor?

>>9148411
Mathematical Logic

Hel p me understand strong mathematical induction pplease

>>9148411
I have physics II and my teacher is already 15 minutes late to class,the retard in front of me talks during the whole class hitting on the girl next to him which is a total slut and already has a boyfriend. She kisses her friends on the lips usually. Today during the day I have to study fucking "Economics" because it was the only thing I could pick to fill 5 days a week of class.
I'm studying to eventually become an engineer.

>>9150224
Musk studied economics along with physics, so that could be a motivation for you, although he doesn't value his economics degree as much

>>9150096
Which kind?

>>9150079
It sucks my man, there's so much time I could have saved simply by having someone who could look over my work.
Asking for help on /sci/ is always my last resort, but it's there when I need it.

Reading the book A = B. Quite fun

>>9148482
>How importand is calculus in AI research
A lot. Just look through some seminal machine learning papers and you'll immediately realize how math heavy the field actually is

That's if you plan on doing actual research though (as opposed to just apply already established algs/frameworks/etc)

>>9149146
GEB to a certain extent

>>9149946
>reddit image
>"mfw T"
>reddit spacing
Fuck off to >>>/r/eddit/

>you have marfan syndrome and other weird deformities
>you have severe OCD and severe social anxiety
>you started trying to learn abstract algebra at 18
>you still can't do most of the basic group theory proofs
>you begin to wonder; you have all of these problems, you probably also have a learning disability
>you might be literally mentally challenged and not even know it
>you begin to consider suicide

it's been 4 years, and i have only managed to memorize thousands of definitions
i give up

I'm trying to teach myself Pre-Calculus. I'm getting stuck at Trigonometry. I've tried enrolling in community college classes but every time I explain that I'm just looking to learn, not exactly get on a degree path they scorn me and shoo me away. I feel like College is designed not for learning outcomes but for pushing the maximum number of students through degree programs.

How do I know if pure math is for me?
I also like physics, but one of the parts about math that I enjoy is doing the proofs. I read Spivak and it was very fun.
At the same time, everytime I see some very advanced mathematics I get discouraged because it seems too unintuitive or abstract to possibly feel rewarding. Is this because I can't understand it yet, or do I have to have the interest before deciding on the pure math degree?

>>9150544
yes. that is what community college is for. graduate programs are for actual self learning. if you want to learn via an institution, you have you put up with their nonsense amd career planning.

>>9150595
you can study physics from the perspective of a mathematician. however, not the other way around. if you like math, then you should pursue that over physics. if you care about jobs: keep in mind that you will need at least a grad degree to have good employability in either.

>>9148576
the derivative is a linear operator on "smooth" functions. being a linear operator makes it a function as well, and thus cannot have 2 outputs.

in brainlet terms: "no"

>>9150544
have you tried MOOCs? (eg coursera, khan academy, etc...)

>>9150638
No. I have no internet at work so I prefer the textbook. I would just like to have a Professor to test me.

>>9150632
Both physics and math are pretty decent job wise in my country. I just want to make sure I will have the interest to make a career. My main concern is that mathematics will stop feeling rewarding the more abstract it gets.
I'm not sure where I got this idea, since so far mathematics has been getting more rewarding the higher up I've been getting. I'm just afraid there might come a point where it's too abstract and essentially meaningless. This doesn't sound very realistic, but it's still a fear of mine nonetheless.

>>9150674
What do you even mean by "abstract"?

>>9150595
You have to solve your avatarfag mental deficiency before even considering such questions.

>>9150427
dont kill yourself mr long fingers

>>9150674
It's actually pretty hard to make a career in either math of physics if you're subhuman (which you seem to be).

>>9150718
>that retarded image
It looks like you didn't even read his post.

>/pol/ talking about axioms
>>>/pol/140340871

>>9150725
Not math related.
>>>/pol/
>>>/b/

>>9150729
What don't axioms have to do with math?

>>9150731
Your post has nothing to do with it, that thread has nothing to do with it either. Discuss pop-sci garbage somewhere else.

>>9150734
What do axioms have to do with pop-sci?

>>9150735
Pop-sci discussion of axioms has to do with pop-sci garbage. Take it to those boards. I might suggest >>>/r/eddit/ as well. It's a good board for your kind.

>>9148863
You'll faill just as you have failed everything in your life fucking loser.

>>9148660
>>9148660
Nothing is stopping you from starting a /c/ thread with that topic.

>>9150742
What's pop-sci about the discussion?

>>9150718
Well the "all plumbers can swim [...]" is a plumber" example is not equivalent to the "kind people are [...] is a socialist" example.
The 2nd example makes sense, but not the 1st.

>>9150751
Read the thread.

>>9150761

>Read the thread.

Which posts in particular?

>>9150770
The ones that say you're gay.

>>9150777

>The ones that say you're gay.

But I haven't posted in that thread, why would the posters be referring to my homosexuality?

>>9150770
>>9150779
>reddit spacing
Use the thread posted above.

>>9150783

>Use the thread posted above.

Which one?

>>9150779
>>9150785
Subhumans aren't welcome in these threads.
Please refer to >>9150729

>>9150786

>Subhumans aren't welcome in these threads.

What's subhuman about my posts?

>>9150718
>>9150754
Rewrite these in logical notation or feel free to fuck off to >>>/lit/

>>9150805

>fuck off

Why the profanity?

>>9150809
>>>/r/taiwan
>>>/r/dogs
Here are some good boards for "people" who have dog-eating friends.

>>9150814

>Here are some good boards for "people" who have dog-eating friends.

Who are you referring to? I didn't think I had any friends

>>9150817
I'm referring to your dog-eating friend.
He is currently on the boards I linked you to, you should join him if you want to live.

>>9150832

>I'm referring to your dog-eating friend.

Who?

>He is currently on the boards I linked you to, you should join him if you want to live.

What's he doing on /r/? Which thread is his?

>>9150770
>>9150779
>>9150785
>>9150794
>>9150809
>>9150817
>>9150833
Filtered.

>>9150833
There was a gook in this thread. He would post anime images and be generally annoying.

>>9150844

>Filtered.

Thanks for letting me know.

>>9150845

>There was a gook in this thread.

Why the racism?

>>9150848
based reddit bro bringing the epic

>>9150845
What was annoying about him?

>>9150845
That gook and his retarded friend are currently hiding in these threads. That won't last for long though as he will be dealt with pretty soon.

>>9150852

>based reddit bro bringing the epic

Np

>>9150854
We'll get them.

How low has this thread fallen

are there any non-brainlets in this thread that actually do math? i read through the posts and it seems like probably no one is more than a freshman

>>9150870
Too bad it's too late to delete it.

>>9150875

>Too bad it's too late to delete it.

Why not just make a new one?

>>9150873
You can't call anyone else a brainlet unless you display your own mathematical prowess.

>>9150882
>You can't call anyone else a brainlet unless you display your own mathematical prowess.
is it worth displaying if the freshmen in this thread wouldn't recognize it?

>>9150882
I am better at Math than you.

>>9150873
Nope, all of them are on your home site.
Here's a link >>>/r/eddit/

>>9150888
how'd u know that was my home site?

>>9150884
It might at least scare the brainlets away, which is a good thing

>>9150891
tru, it'd be nice to see some actual math in this thread even though we're 100 posts in

>>9150886
Prove it

>>9150896
I have memorized the first hundred digits of the mass of your mom.

>>9150882
>You can't call anyone else a brainlet unless you display your own mathematical prowess.
Why not?

>>9150898
That's trivial

>>9150900
Because you are a dumb fuck as demonstrated by some of your previous posts.

>>9150902
>Because you are a dumb fuck as demonstrated by some of your previous posts.
How so?

>>9150901
Ok then
I can make a perfect Vulcan salute

>>9150909
Pretty impressive. I'm sure >>>/r/eddit will like it

Just love it when newfags tell me to go to Reddit because they don't realize all the oldfags went to Reddit and began to appreciate it after 4chan went to shit. In other words they're trying to fit in. It's cute. Please just keep doing it.

>>9150919
What's there to appreciate in reddit? If you like it that much, you should stay there.

>>9150919
the 'go to reddit' is just a recent /pol/ and alt-right meme, it's a good giveaway though to know that someone only came to 4chan in the past year or so since that's when reddit randomly started becoming demonized here

>>9150925
go back there

>>9150925
see >>9150924 >>9150915

>>9150934
how come?

>>9150919
>""newfags""
>""oldfags""
see >>9150915

>>9150948
aren't those 4chan words?

>>9150966
yes

>>9150982
that's what i had thought at least

>>9150983
how did you know?

Redditors are always welcome.

>>9150985
past experience

>>9150988
>Redditors are always welcome.
agreed, the next thread should be more welcoming to redditors and anyone else from other websites

>>9150870
It was thanks to anime posts like yours

>>9150994
what's wrong with anime?

isn't 4chan an anime website?

>>9150995
It's disgusting crap liked by virgin neckbeards.

On topic: How does /mg/ visualize complex vector spaces? Surely the complex plane is misleading? You would expect multiplication by i to be rotation by 90 degrees but in fact in a complex vector space it's just multiplication by a scalar.

>>9150995
>what's wrong with
anime is cancer.
>isn't 4chan an anime website
no it isnt. this is a science & math board. if you want to post retarded virgin anime please fuck off back to >>>/a/

>>9151002
>Surely the complex plane is misleading?
not if the vector space is one dimensional

>>9150999
>It's disgusting crap liked by virgin neckbeards.
then why are you on an anime website?

>>9151002
Kill yourself retard.

>>9151005
>no it isnt. this is a science & math board.
feel free to start posting some science and math then

>>9151008
>>>/a/

>>9151012
yes that's the anime board

>>9151014
Yes, and you belong there weeb

>>9151017
i'm not a weeb though i don't watch anime

>>9151026
>i don't watch anime"
Spotted the redditor.
Fuck off to >>>/r/eddit/

>>9151046
i'm too busy doing math to watch anime these days

>>9151064
kys

>>9151074
>kys
is this board 12?

>>9151077
no but the girls who i have sex with are

>>9151005
>anime is cancer.
Good, use >>>/r/eddit instead of an anime website then.

>>9150204
It's induction with more than one base case, essentially. The pattern you need may not hold for n=1 so you do more cases until you can properly move on to your induction step

>>9151101
ill induct your ass with my dick

I'm too busy watching anime to do math

>>9151006
complex vector space can't be one dimensional??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????

>>9150204
you cna't be old enough to use this sight

>>9151185
>complex vector space can't be one dimensional??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????
Wrong. Given any field and any integer n >= 0 there exists an n-dimensional vector space over that field.

>>9148411

When did "real math" begin?

It's gotta be 17th-18th c. sometime, right?

>>9151194
define "real math"

>>9148791
its good shit to know

>>9150354
that's probably my favorite book. It's good on understanding formal systems, but isn't very rigorous. 11/10 philosophy though.

>>9151185
everyone laugh at this sucker who doesn't even know who Hilbert is

>>9151193
>>9151207
i thought C was isomorphic to R^2
we ignored complex vector spaces in class

>>9151235
>i thought C was isomorphic to R^2
as vector spaces over [math] \mathbb{R} [/math] yes

>>9151242
okay so a vector space C over C is one dimensional with a basis as any nonzero element of C
but a vector space C over R is two dimensional with a basis similar to 1, i

BUt, a vector space C over R is not a complex vector space yeah?

>>9151257
>BUt, a vector space C over R is not a complex vector space yeah?
yes

>>9151257
>BUt, a vector space C over R is not a complex vector space yeah?
"over R" means that it is a real vector space. They're synonyms.

>>9150544
What book? Doing Cohen right now

>>9148411
I dont get how from power series derived the formula for finding e^x for any x.
What should i must read?

>>9150544
What in Trig is giving you a hard time?

>>9151194
At least with the greeks (if you don't think classical geometry is og, then you probably should look again)

why doesn't quantum mechanics use mathematical notation?
i struggled with that shit for 2 years and then i realize it's literally just obfuscated linear algebra
wtf

>1+2+4+8+... = -1
BRAVO HENSEL

What car do you guys drive

>>9151257
the scalar field is part of the definition of a vector space. you have to distinguish between two different vector space structures on the set C of complex numbers - its structure as a complex vector space, with respect to which it has dimension 1, and its structure as a real vector space, with respect to which is has dimension 2

Is Statistics II supposed to make any sense at all?

>>9151708
rigorous statistics makes sense, but the kind of statistics they throw at bio majors doesn't.

you can tell the difference by asking yourself the following question, "have I seen a gamma function yet?"

>>9151453
[math]12^-s + 11^-s + 10^-s + 9^-s + 8^-s + 7^-s + 6^-s + 5^-s + 4^-s + 3^-s + 2^-s + 1[/math]

Hey /sci/ what are some great undergrad/highschool (Calc, algebra, analysis etc.) books made in 21st century? All I see here are mostly "old gems" but haven't really seen any good recommendations on books made after year 2005

>>9152026

>>9152026
For last seventeen years in newton-leibnic formula find errors?

Or mathematics for last twenty years find a way how in analitycally way compute transition conditions of laminar flow transform to turbulent flow of the liquid in pipe for all possible speed/liquids/pipe?

9am vector calculus

>>9151194
I don't know when it began, but it became comfy with complex analysis

How do I motivate myself to study for Calculus 2? It's so much fucking work and completely unrelated to my field. I find it entirely uninteresting and it's like double the work of any of my other classes.

I'm currently taking a real analysis course, and I feel like I've hit a spiky wall. I can barely understand anything, and I don't know how to approach the exercises and how to prove them.
Though I understand everything covered in class.
The book we're using is Principles of Real Analysis by Rudin and Apostol's Mathematical Analysis as a reference.
I borrowed a "workbook" today that was supposed to be supplementary to the book by Rudin, but it turned out to be made for another book by the same name but different author (By Aliprantis). My question is, is there any such book by/for Rudin? Couldn't find anything online.
Also, any tips would be greatly appreciated.

>>9152532
>I can barely understand anything
Anything that's in the book, I should add.

>>9152532
Read Zorich or Tao before going for Rudin. It's a good book, but it's terrible for self-study.

Greetings /sci/, I am trying to teach myself linear algebra and I would like to know if what I understood from linear combination is correct:

I can't write v=(3,2) as a linear combination of u=(1,-2) and z=(-3,6) because they are "parallel".

That's what I understood from it

>>9152527
>completely unrelated to my field
What field?

>>9148847
For propositional logic you can honestly just learn the rules yourself

>>9152026
How the fuck is this for undergraduates?

>>9152255
What? I'm not talking about flaws, point of the books are so people learn math

>>9152035
How the fuck is this for undergraduates?

>>9152255
What? I'm not talking about flaws, point of the books are so people learn math

>>9153176
>How the fuck is this for undergraduates?
How is it not? It's literally an entry in Springer's 'Undergraduate Texts in Mathematics' series

>>9152656
>I can't write v=(3,2) as a linear combination of u=(1,-2) and z=(-3,6) because they are "parallel".
It's not enough to just say they are parallel, you need to show the equation v=au+bz has no solutions

I need more M/a/th

Why Laplace transformation has to use s as a complex variable instead of just a real variable? me no understand

>>9154246
because laplace transforms relate real variables with complex ones

Laplace transforms are one of the main fundamentals of electrical systems, which is neat

>>9150754
>Well the "all plumbers can swim [...]" is a plumber" example is not equivalent to the "kind people are [...] is a socialist" example.
The author successfully demonstrates the same fallacy in each example. It makes perfect sense

>diagonalisation arguments

Why do math books rarely drop in price.. I have a wishlist of math books totalling around 15-20 and every so often I will check the prices on second-hand book sites but they stay fixed at silly amounts. I only use ebooks as a supplementation or if I absolutely don't intend to buy the physical book. What do guys?

How do I get good at math? This is my frist time visting /sci/ and shit here is creeping me the fuck out.

HELP ME MASTER COLLEGE ALGEBRA AND ITS CONCEPTS OR ILL KILL MYSELF?!?!?!?!?!

>>9150289
The mathematical kind.

any update on whether yamashita's exposition cleared anything up?
http://www.kurims.kyoto-u.ac.jp/~gokun/DOCUMENTS/abc_ver6.pdf

>>9154745
You know it's going to take more than a few days to read 300 pages of heavy research level math.

>>9152026
Tao Analysis I & II, and Pugh's Analysis book are good and recent books.

>>9154748
>You know it's going to take more than a few days to read 300 pages of heavy research level math.
Fair enough, it would help to know where exactly the experts got stuck on the original 500 page publication

>>9154745
no because inter unviersla techimiouler theory or whatever mochizuki says is a scam

>>9154769
>no because inter unviersla techimiouler theory or whatever mochizuki says is a scam
how so?

>>9150427
post hands

>>9154810
Communicating badly and then acting smug when you're misunderstood is not cleverness.

>>9154842
>Communicating badly and then acting smug when you're misunderstood is not cleverness.
What does that have to do with the image?

>>9153547
thank you

*kills myself*

what are the prerequisites to learning abstract algebra?

i really like algebra and thought abstract algebra would be a good thing to learn.

i only have knowledge of high school maths (no calculus).

>>9155362
>what are the prerequisites to learning abstract algebra?
nearly nothing, know what a set is

pic related is easy-going (starts with integers and polynomials)

Where do I learn hilbert spaces, Fourier shit and all the jist for QM?

>>9150224
uma delicia

>>9148411
OxfordAnon, if you're here: how do I get out of the hellish 50-60 MAT score range? Just chugging through past papers doesn't help.

Also, how intensive and time-consuming is the coursework?

How do I stop wanting to kill myself every time I do homework? I have to take through Calc 3 to graduate so I have to get through it somehow

>>9148411
Spent the bulk of my math time prepping myself for representation theory. Shits cash

What is the best "non-engineer" calculus book? Spivak?

Currently reading this fat baby, I recommend for people like myself who want to self study a bit of maths.

>>9150743
Wow man, that's messed up.

>>9155630
This is a highschool textbook. Burgers truly are cucked.
>>9155625
Tao's anal. If you're burger and didn't learn calc during highschool, just skip it and go straight to anal. Tao's book is amazing for self-study, it's easy in the begginning and slowly picks pace. Also, there are no prereqs for it, as in everything that you need is covered in the book, rigorously enough.

>>9155662
>This is a highschool textbook
Haha...

>Burgers truly are cucked.
I'm French.

>>9155662
I looked at the contents and it seems like what I need, thanks.

Have you any cool wallpapers related to math?

>>9155692
But... cats don't lay eggs?

>>9155840
Look at the picture above, that's the proof.

Is it possible to develop an occult field of math?

>>9155854
Yes, just look at Cantor.

>>9148411

What should I be studying?
I have nothing past highschool.

>>9156311
Analysis if you are gay, Algebra otherwise

>>9148411

Doing review of algebra and trigonometry for Calculus I...

Baby steps...

>>9151194
Euclid's Elements

>>9152532
At a certain level it just takes time. Really meditate on the definitions. Memorize them even if you don't understand them and really try to parse through them mentally when you find yourself idle. Read theorems and problems before bed and when you wake up you might find an epiphany.

Can someone give me a straight answer on Spivak vs Apostol vs Stewart vs Courant vs Rudin? What are the differences in these books?

>>9156388
Stewart focuses on calculating.

Spivak and Apostol are rigorous in what they present but keep it less general.

Rudin is full blown generality.

Haven't read courant.

>>9156388
Rudin is a meme

consider a function f that is continuous over interval [a,b] where f(a) < 0 and f(b) > 0, why f(x) = 0 must.
isnt the description the proof itself?

>>9156397
>>9156401
Can you be a little more specific? I'm inclined towards Stewart right now since you said it focuses on calculating.

>>9156421
Sure.

Stewart is better if you want to focus on the technique of solving calculus problems. The book explains things mostly by intuition with proofs here and there. There is an insane amount of problems that all boil down to calculating the value of something. Thats why this book is a great introduction to the ideas and geared towards engineers and scientists.

Spivak and apostol focus on calculating as well, but they are rigorous in their presentation of all of the material. There's more problems focused on proving properties of calculus. The focus is shifted towards understanding calculus versus being able to use it practically.

Rudin is solely meant for understanding the concepts. Its as general as possible.You will be proving properties of calculus and you will be solving classes of problems instead of just calculating certain values.

>>9148847

>trying to explain

why are you so sure she knows what she's talking about?

>>9156408
no, that's just your laziness talking

>>9156517
Thanks a lot. Stewart really seems like the best one for me. Is the material in the book by these authors the same though? I mean that does Stewart cover everything that the other books do but it isn't as rigorous and proof based as the other ones, right? Also, Stewart has many books on Calculus, which one should I start and end with for learning Calculus til an undergraduate level or even graduate level too just in case I decide to go deeper?

>>9156566
Stewart will cover less calculus than spivak and apostol and those two will cover less than rudin. Any Stewart book will do on calculus.

If you want to go to the graduate level understanding. I would skip stewart. Go read a book on proofs like "how to prove it" by velleman and then dive into spivak or apostol. I'm partial to apostol and his sequal volume but its up to you. You will understand calculus much better than if you did stewart.

Then go after rudin and if you get stuck on rudin, cross reference with apostol's analysis book.

Starting to get into the nitty/gritty of calc 3. Yesterday we were introduced to derivatives of vector functions, and now today we learned about arc-length of vector functions. But so far everything just seems like stuff we already know, just in a different form, like
[math]
\left | \overrightarrow{r}(t) \right | = \int_{a}^{b} \left | \overrightarrow{r{}'}(t) \right | dt
[/math
Is just the normal arc-length equation just disguised with different formatting.

How much harder does it get, anons?

>>9156607
it's as hard as you wanted it to be
studying some thermo right now and I'm 100% the fact that I didn't learn anything (but passed) means i didn't put enough effort into mastering the art
It's easy to solve baby problems, but to really apply that shit I wish I didn't blow off calc3; specifically the art of proofing

If I have two functios f and g sucha that their product fg is a polinomial then both of them need to be polinomials?

>>9157037
come on brainlet, think

Studying momentum

bout to finish some calc iv homework, feels good man

but have a calc iv test this Monday and anther test Wednesday so entire weekend will be studying instead of relaxing :^(

>>9154559
Regular books drop in price because there's very high demand at launch and then 12 months later nobody cares, so they're cheaper to reflect that.
Math books don't have a launch audience unless it's some breaking-news monograph; their demand is mostly constant which is reflected in a constant price.

I want to know ALL of the morphisms!

-morphism
-epimorphism
-endomorphism
-monomorphism
-homomorphism
-isomorphism
-automorphism (above: with regard to algebra, and variously incorporating the notions of injection, surjection, bijection)
-holomorphism (with regard to complex derivatives)
-diffeomorphism
-homeomorphism (with regard to topology)

What are ALL of the morphisms anons? Tell me more! :D

When working modulo $m$, the notation $a^{-1}$ is used to denote the residue $b$ for which $ab\equiv 1\pmod{m}$, if any exists.

For how many integers $a$ satisfying $0 \le a < 100$ is it true that $a(a-1)^{-1} \equiv 4a^{-1} \pmod{20}$?

How on earth do I solve this?

>>9157236
Reformatted:

When working modulo [math]m[/math], the notation [math]a^{-1}[/math] is used to denote the residue [math]b[/math] for which [math]ab\equiv 1\pmod{m}[/math], if any exists.

For how many integers [math]a[/math] satisfying [math]0 \le a < 100[/math] is it true that [math]a(a-1)^{-1} \equiv 4a^{-1} \pmod{20}[/math]?

>>9148411
Differential forms. Also why do tensors look so ugly in physics books? The concept seems to beautiful and yet all that dread complicated notation...

>>9157239
[eqn]a(a-1)^{-1} \equiv 4a^{-1} \pmod{20}[/eqn]
[eqn]a \equiv 4a^{-1}(a-1) \pmod{20}[/eqn]
[eqn]a^2 \equiv 4(a-1) \pmod{20}[/eqn]
[eqn]a^2-4a+4 \equiv 0 \pmod{20}[/eqn]
[eqn](a-2)^2 \equiv 0 \pmod{20}[/eqn]
Therefore, 20 divides (a-2)^2, which means 2 and 5 divide a-2. Hence [math]a \equiv 2 (mod 10)[/math].

But technically, [math]a^{-1}[/math] and [math](a-1)^{-1}[/math] have to exist mod 20, which means both a and a-1 are coprime to 20. Which is impossible as either one of them has to be even.

hey /mg/

I am a retard who didn't go past alg 2 in high school and have to retake it in college. I can't find help anywhere else.

Can you guys help me solve this system of 3 3-variable equations?

41x + 58y + 75z = 4370
x + y + z + 90
41x = 3 * 58y

x, y, and z are all supposed to be whole numbers.

>>9156553
no bully pls, i am just curious, taking math as a hobby

>>9157037
>If I have two functios f and g sucha that their product fg is a polinomial then both of them need to be polinomials?
No.

>>9153176
>Computational algebraic geometry and commutative algebra

I can easily see this being undergraduate level.

>>9156576
Does Stewart cover multi variable calculus? I want to learn calculus from 1 til 3.

What level of math or topics in math do I need to know before I can understand a book like Von Neumann's Theory of Games and Economic Behavior?

>>9148426
Same here senpai

Biochemistry of central dogma desu

>starting HNC in Electronics in two weeks
>tutor sends me some pre revision
>calculus and other shit
>mfw haven't done maths since GCSEs 8 years ago and never did calculus
>trying to learn how to do it involves me going back to algebra because I've forgotten, algebra involves fractions which again I can't remember how to do

I'm fucked, I have no problems learning but I need to learn a hell of a lot quickly.

I'm using Khan Academy which I like, but can you help me with this one? I keep getting 7 1/6 which is wrong and I don't know why.

I have a function [math]f:\mathbb{R}^n\rightarrow \mathbb{R}^n [/math] such that [math]df_{x}[/math] is am isometry [math]\forall x\in\mathbb{R}^n[/math]I know that it also preserves inner products so I have the identity [math]<df_{x}(u),df_{x}(v)>=<u,v>[/math] and now I need to prove that:
[math]<d^2f_{x}(u,w),df_{x}(v)> + <df_{x}(u), d^2f_{x}(v,w)>=0[/math]. My knowledge of functional analysis is limited but my professor told me to just use "the product rule", but with respect to what? The "second derivative" its actually the differential of a function that goes from [math]\mathbb{R}^n[/math] to[math]\mathcal{L}(\mathbb{R}^n,\mathbb{R}^n)[/math] So what Im trying to do is define a Bilinear map that takes as input differentials at some point and output a bilinear form. Something like [math]\phi:Im(df)\rightarrow B(\mathbb{R}^n\times\mathbb{R}^n,\mathbb{R})[/math], with the codomain being the space of bilinear forms such that I can define the map as[math]df_{x}\mapsto<df_{x},df_{x}>[/math] and then aply the product rule given in banach spaces for continuous bilinear maps. But I repeat my knowledge of these topics are very limited and I don´t know if I´m assiming shit or if my functions are well defined. Help plox.

>>9158424
You are beyond help

>>9158233
I highly recommend switching to "analysis on manifolds" by Munkres. Don't be turned off by the title, it's just multivariate calculus at the level of Stewart, but by a non autistic author.

>>9158474
Please help me

>>9158477
For starters you are only meant to multiply the variable value by the numerator in your example, I don't know how you are even getting mixed numbers

>>9158482
So it's 12/2-3+15/3=6-3+5=8?

Prob and stats, Complex and Real analysis also Differential Geometry desu
>300k starting major

>>9158439
Ok, maybe I need to tweak some thing like the domain of [math]\phi[/math] it mustb be all [math]\mathcal{L}(\mathbb{R}^n,\mathbb{R}^n)[/math] because the former isn´t even necesarilly a banach space. So what I have is that for every element in there that is a differential of [math]f[/math] then [math]<df_{x},df_{x}>=<Id,Id>[/math] So the function in this values is "constant" in termos of the bilinear form they output so the derivative must be 0? I think my professor doesn´t want this level of formality but I don´t know how to move forwards otherwise.

>>9158486
Yes. I suggest you actually watch the videos if you don't know how to do the exercises. Also I believe you can ask for hints when you can't solve a problem

>>9158491
>>9158439
Fugg I think the domain needs to be [math]\mathcal{L}(\mathbb{R}^n,\mathbb{R}^n)\times \mathcal{L}(\mathbb{R}^n,\mathbb{R}^n)[/math]

>>9158424
LOL WHAT THE FUCK
ELECTRONICS
CANT Do FArCTIONS
DUDE EVERY > YOU MAKE THE SITUATION GETS MORE COMICAL BY TEN

>>9158439
>what the fuck is ϕ
>What the fuck is L
>↦
what
i feel like this anon
>>9158424

>>9158506
Maybe I´m not making any sense but do you know functional analisis?

fluids man... fucking fluids.

>>9158439
>I have a function [math]f:\mathbb{R}^n\rightarrow \mathbb{R}^n[/math]
No you don't.

>>9158511
Nope-
when did you learn that
kek i feel retarded

>>9158525
I´m actually just fucking around with different pdfs on the "frechet derivative" which I a way to assign a derivative to more abstract functions in abstract vector spaces called "Banach spaces" shit´s interesting af, but I haven´t taken any course or properly read a textbook.
>>9158520
You don´t know me, plx help though :(

>>9158475
What do you mean? I should use Stewart for Calculus I and II and then "Analysis on Manifolds" for Calculus III?

Antiderivatives this period. They're kinda fun desu.

>>9158475
>>9158538
Also, what's the difference in early transcendental, essential calculus and the standard calculus book by Stewart. Is Stewart's multi variable calculus book really that bad?

>>9158439
[math]\mathbb{R}^n[/math] can't really be shown to exist.

>>9158513
ur sexist for finding fluids difficult

I largely don't give a fuck about doing math for it's own sake, are there any subjects I should avoid that have zero real world applicability, or is that not an issue at undergrad level?

>>9159002
>is that not an issue at undergrad level?
That's not an issue at brainlet level (which is the maximum your kind can hope to achieve), so you should be fine.

>>9159019
t. mental masturbation pro

>>9159074
No, even an engineer can call himself a "pro". I have a doctorate in mental masturbation and from now on I demand you refer to me as that. Dr. Anon for you.

>>9158538
>>9158551
BUMP

>>9158439
differentiate with respect to x

>>9160736
THAT MAKES NO SENSE WITHOUT FUNCTIONAL ANALYSIS. I WANT IT TO BE RIGOROUS REEE.

Can someone help me understand these "summation"s over AND and OR?

>>9150718
the second example is logically valid though

https://discord.me/maths

Proper Mathematics Discord server based on ArXiV ontology.
Professional server, no shitposting allowed.

Can someone post that iceberg/deep sea math pic?

>>9161231
>based on ArXiV ontology
What is this supposed to mean?

>>9161250
Channels are named after categories found in: https://arxiv.org/archive/math

>>9161171
What are you confused about?
The first paragraph says "There are 9 x 9 x9 = 729 such propositions, as i, j, and n all range from 1 to 9".

The "summations" are just the ranges found in cell, row, or column.

pls recommend textbooks for multivariate calculus and vector calculus

>>9161231
Fuck off to >>>/r/eddit/

>>9161303
>Fuck off to >>>/r/eddit/
"no"

I see, it's that subhuman. I not surprised in the slightest.

>>9161272
I understand what they mean macroscopically, but I want to deeply understand the meaning/order of the summation.

>>9161354
>>9161303
>>9161305
>>9161258
answer my number theory question in the discord

>>9161389
see >>9161303

>>9161389
>answer my number theory question in the discord
post it here

>>9161389
>disc*rd
Sorry, I'm not a retarded gamer/redditor. Post it here if you want a real answer.

>>9148411
studying intro topology (mainly set theory for now)

>>9158203
can't you just use the trivial case i.e. 0/1

I will start reading University Physics with Modern Physics, I just hate that my brain forgot many identities.

I will do this out of love for the subject, the fascination that some subjects trigger, primarily acoustics, electromagnetic theory and the meme quantum theory.

I want to prove everything with equations and not just be a brainlet who can only spout what he saw on a Discovery Channel documentary or shit like that.

>>9161400
>>9161415
>>9161433
Consider the following problem:

For how many integers a satisfying 0 <= a < 100 is it true that

[math]a(a-1)^{-1} \equiv 4a^{-1} \pmod{20}[/math]?

Here's what I thought: multiply by [math]a(a-1)[/math] to get

[math]a^2 \equiv 4(a - 1) \pmod{20}[/math]

We see that

[math] a^2 - 4a + 4 \equiv 0 \pmod{20}[/math]

which implies

[math](a - 2)^2 \equiv 0 \pmod{20}[/math]

So we need a perfect square whose root is a multiple of 20. The only such squares that exist are 0^2, 20^2, 40^2, 60^2, 80^2.

So the answer is 5 integers?

>>9161501
Of course, in this context, [math]a^-1[/math] denotes the modular inverse of a.

>>9161479
>can't you just use the trivial case i.e. 0/1
what...

>>9161027
what functional analysis ? you want to differentiate the function x -> (df_x(u), df_x(v)) (with u,v fixed)
You may rewrite this as the composite g o df where g maps a functional x* on R^n to <x*(u), x*(v)>. Then, you apply the chain rule

>>9161500
>>>/sci/physics

>>9161501
>So we need a perfect square whose root is a multiple of 20.
Wrong, think about this again

>So the answer is 5 integers?
Even if the above was right, this would also wrong

use more rigour

>>9161521
Why? The field is described through mathematics, for instance I will use calculus, linear algebra, and algebra to describe several phenomena, why would it not be related?

>>9161530
It's related as long as you discuss the mathematics it's described through. Your post doesn't have anything to do with mathematics.

>>9161529
>use more rigour
It's number theory. That's like saying "use more rigour" to a physishit.

>>9161518
Yea, the chain rule which implies you need to take the derivative of a gun that goes from the space of linear transformations to R^n and a function that goes from R^n to the space of linear transformations which is not as trivial as you say. I need at least the theorem of the derivative of a bilinear map.

>>9161501
this is >>9161529 again
your question is actually trivial from the first equality mod 20, stare at it and see why

>>9161557
Well yeah, but you can rederive it. I usually go back to the definition when it gets a little (but not too) complicated (which is the same as reproving the chain rule in a special case).
Let [math]\phi(x) = \langle df_x(u), df_x(v)\rangle[/math]. Let h be any vector. We may write (by definition) [math]df_{x+h} = df_x + d^2f_x(h, \cdot) + \text{(higher order terms)}[/math].
Hence [math]\phi(x+h) = \langle df_x(u) + d^2f_x(h,u) + (higher order terms), df_x(v) + d^2f_x(h,v) + (higher order terms) \rangle[/math] and, expanding, [math]\phi(x+h) = \phi(x) + \langle df_x(u), d^2f_x(h,v)\rangle + \langle d^2f_x(h,u), df_x(v) \rangle + (higher order terms)[/math], hence the derivative is what you first wrote (we could make the "higher order terms" thing more rigorous with Landau notation)

>>9161606
Well I think there´s still some non trivial issues with the higher order terms because in your first expansion of [math]df_{x+h} = df_x + d^2f_x(h, \cdot) + \text{(higher order terms)}[/math] you have those higher order terms that are still moving in the space of linear transformations and when we say those terms go to 0 as h goes to 0 it means in the sense of an operator norm. I suppose than to prove that the higher order terms in your second expresion you just need to consider the inequlatiy between an the norm of a linear operetor evaluated at a point and the product of the operator norm of a function and the norm of the point. I suppose that my point now is that it´s pretty bullshit to treat it as some basic calculus problem.

Any good resources for combinatorics? I never saw this in highschool and I need it right now.

>>9148411
Probability.
It doesn't help that my professor is Asian and assumes we are all Asian levels of good at math.
>tfw dumb American

>>9148411
[math]0 \longrightarrow M \overset{\varphi}\longrightarrow N \longrightarrow \mathrm{coker} \, \varphi \longrightarrow 0[/math]
I have this exact sequence of modules and I'm reading a proof of the sequence being split iff [math]\varphi[/math] has a left inverse.
I might be retarded, but can someone explain how [math]\ker \psi[/math] got involved here? Is it isomorphic to [math]\mathrm{coker} \, \varphi[/math]?

>>9148847
there's a bunch of youtube series on propositional logic.
https://www.youtube.com/watch?v=qV4htTfow-E&list=PL619166130C21EADA

Discrete math \ probability

Having a lot of fun exploring my first integrals in calc II! I might even read ahead this year!