/mg/ - Math general

[Anonymous No.9130842]

No physishits edition.

What are you studying, /mg/?

[Anonymous No.9130843]

i'm teaching calc 2 this smester hbu?

[Anonymous No.9130845]

Mathematically, on a scale of 1-butthurt how assblasted are you about your threads being constantly shit.

[Anonymous No.9130877]

>>9130842
Generatingfunctionology, good book

[Anonymous No.9130889]

Does anyone here know any decent math books that cover all the topics present in the art of problem solving books: volume 1 and 2?

I already have the first book but can't seem to find the second one anywhere so I think I will have to give up on this series.

Here's the list of contents of the 2 two books:
>Vol .1
https://s3.amazonaws.com/aops-cdn.artofproblemsolving.com/products/aops-vol1/toc.pdf

>Vol. 2
https://s3.amazonaws.com/aops-cdn.artofproblemsolving.com/products/aops-vol2/toc.pdf

If something like this is impossible then what are the best books for teaching yourself mathematics from the basics till prealgebra and precalculus.

Thank you.

[Anonymous No.9131498]

>>9130843
uh, op said no physishits. unless you're in middle school, in which case, underage!!!

[Anonymous No.9131502]

>>9130842
>linear algebra and discrete math
we're doing problems from Raymond Smulyan's books in discrete to begin the semester. He's my new math husbando.

[Anonymous No.9131506]

>>9130889
>http://libgen.io/search.php?req=9781934124109&open=0&res=25&view=simple&phrase=1&column=series
You're welcome.

[Anonymous No.9131518]

Unitl you accept it.

[Anonymous No.9131523]

>>9130889
>>9131506
Although I should point out that the AoPS books are supposed to accelerate students through the math curriculum while also teaching them techniques for math competitions. If you're not going to do math contests, I think this is a bit of waste of time. Gelfand's books usually get recommended, or Lang's Basic Mathematics. At this level, the book isn't super important as long as you choose one an stick to it.

[Anonymous No.9131534]

How does /mg/ prepare to give talks about their research?

I'm an undergrad math major but a while back I discovered some theorems (really simple but in my opinion interesting) and I showed them to a professor. After not hearing anything from him for like two weeks and mentally convincing myself that my findings were trivial and unimportant and that I wasted his time by merely showing it, out of nowhere he comes and tells me he signed me up to give a talk to the entire department about my findings and I am going crazy.

I am nervous because I am shit at explaining myself and talking in front of crowds. I am nervous because maybe someone will find my findings trivial. I am nervous because there is a question round and if someone asks me "Are there any applications to this?" I will have to say no, that what I showed them is unfiltered autism.

I've never been so nervous in my life. Math used to be a lonely endeavor but now I'm supposed to expose by flawed self to the local mathematical community. How do I do this without making a disgrace of myself?

How have others dealt with this? I've been here and I know most of you are as autistic as me so you must have felt like I am feeling now. How did you cope? How did you not break?

[Anonymous No.9131540]

>>9131534
This is hilarious.
Practice giving the presentation to some friends. The professors will know your an undergraduate who hasn't done this before, they're not going to go out of their way to break you. Giving good talk is a skill developed only after lots of practice (and plenty of successful mathematicians never learn it unfortunately). Do your best and don't worry about it, it won't make or break the rest of your career, your work will speak for itself.
Also, anyone who asks "are there applications" at a pure math talk doesn't belong in the room.

[Anonymous No.9131542]

>>9131540
>The professors will know your an undergraduate who hasn't done this before
>he/she doesn't have that one superserious mathematician in his department who will grill every student irregardless of years of study
Lucky

[Anonymous No.9131543]

>>9131498
>teaching a math class
>math grad student
>somehow not math related
Ban me if you're so pissed

[Anonymous No.9131553]

>>9131540
>Practice giving the presentation to some friends.
This is where I'd put my trophy... IF I HAD ONE

>they're not going to go out of their way to break you.

I know, I am just scared because the professors who know me hold me in very high regard. I am worried that because of this they will have very high expectations about what I discovered and then when I present my findings their expectations will shatter. All is relative after all. If I was retarded then I wouldn't have to worry about this, but because all of them trust me there is a chance that they are expecting something better than what I will present.

But I get your point. It is just that for the past years I have been in a perfect bubble in which I have not had to do anything other than do math, the one thing I'm good at. And now out of nowhere, my bubble was burst and I'm supposed to pick myself up and not fuck up.

Last time I had to give speeches was high school and I've got lots of bad memories. Math was supposed to protect me from those kinds of interactions but here they are again.

[Anonymous No.9131677]

>>9131506
>>9131523
Here's the list of contents for that book:
https://s3.amazonaws.com/aops-cdn.artofproblemsolving.com/products/intro-counting/toc.pdf

As you can see, content-wise it's not even close to volume 2, it's just - as the name would suggest - an introduction to counting and probability. Volume 2 covers everything from quadrilaterals to matrices and sequences and series.

I already have Lang's Basic Mathematics and it seems like a great book but I want a book that can help me learn math from the very basics like exponents, logarithms, sets, roots, etc. Gelfand's books seem like shit to me, instead of explaining anything he just starts with problems, at least that's how his Algebra book is like.

Also, please don't recommend Khan Academy or some other pathetic shit like that. I want to learn from books.

[Anonymous No.9131688]

>>9131518
Right and wrong. Those mathematicians that dislike the supposed "lack of rigor" in physics should also reject statements proven assuming generalized RH/CH.

[Anonymous No.9131690]

>>9131518
Accept what? The vast majority of phyishishits being math illiterate? I think that's already pretty well accepted. It's fine though, not everyone is capable of doing mathematics.

[Anonymous No.9131748]

>>9131690
Not everyone is capable of doing physics either or else all mathematicians would be skilled physicists.

[Anonymous No.9131768]

>>9131748
that's not about capability. physics requires a lot of time to invest in it. math is broader than physics. you can't just say "hey you're a physicslet because you do math" because a mathfag can say the same to a physicist who doesn't know about algebraic geometry and deformation theory, even though knowing those things could help simplify problems. knowledge is a double edged sword. you might win. you might waste time. but you gotta swing it down on a problem at some point.

how much math do you need to solve a problem? how much physics do you need to understand a problem? how do you answer these?

[Anonymous No.9131798]

>>9131518
>reproducible experiments = rigor
>something happened 5 times => it will happen always

are physicists even real people

[Anonymous No.9131805]

dont wanna make a thread for this, maybe it fits into math general because statistics or something?

what would be the minimum number of humans you'd need to re-create humanity after theyve been wiped out, and what ratio of male to female? assuming no epidemics, natural disasters etc
and optimal fucking

[Anonymous No.9131806]

>>9131805
At least 500

[Anonymous No.9131812]

Reposting from old thread:

Hi, I'm relearning math from scratch. I've started with Kiselev's Geometry I. Is it a good choice? If no, what are alternative geometry books?

[Anonymous No.9131895]

>>9131798
It's actually provable in any consistent formal system that they are not people.

[Anonymous No.9131899]

>>9131748
Any non-retarded mathematician is capable of doing it. It's just not needed the way physishits need math.
Most of us simply don't waste time on such vapid garbage.

[Anonymous No.9131907]

>>9131812
I was doing Trig when I noticed I remembered fuck all from elementary geometry, currently going through "Elementary Geometry for College Students" by Daniel C. Alexander.
Currently not very far in, but it doesn't look bad.

[Anonymous No.9131964]

fusion categories + potential relationship with quantum symmetry groups

[Anonymous No.9132020]

So I fucked up.
I fell into the CS meme, despite me showing excellent ability into mathematics during my high school years, I thought I was going to need a good paying job to pay my bills.
Somewhere in the 4 years I decided to double major into mathematics and I really liked it, but for talked out of completely switching majors because I was already in too deep into my CS meme.
As I have good grades I decided I wanted to go into grad school, but to be honest not many topics in CS inspire me. I was thinking of actually getting a PhD in applied mathematics, but I don't know if I have enough """mathematical maturity"""

[Anonymous No.9132039]

>>9132020
>"applied mathematics"
>"meme"
Your kind isn't welcome here
Reddit might be a better choice for you.

[Anonymous No.9132046]

>>9132039
What's wrong with apple math?

[Anonymous No.9132048]

>>9132046
There's nothing wrong with fiction. But there's >>>/lit/ for that.

[Anonymous No.9132052]

>>9132046
He's an edgy high schooler

[Anonymous No.9132092]

>>9131899
Lol no. You don't even know how retarded mathematicians get when solving even basic physics problems.

[Anonymous No.9132093]

>>9132020
>applied mathematics
begone redditor

[Anonymous No.9132095]

>>9132092
>Lol no.
>>>/r/eddit/

[Anonymous No.9132115]

>>9132092
back to your physics containment thread, physiplop.
>>>9116664

[Anonymous No.9132122]

>>9132039
>>9132093
>>9132095

Why is 4chan so obsessed with Reddit? This mindless shitposting only worsens quality of the board. If you are not going to engage with an argument then don't reply at all.

[Anonymous No.9132131]

>>9130842
Can someone point me to literature about subobject classifiers?

[Anonymous No.9132138]

>>9132092
It's not the actual problem solving, but for me reading physics textbooks is impossible. My experience with physics:

>looks up some physics books
>reviews: "mathematically rigorous", "perfect for mathematicians wanting to learn physics" etc.
>gets the book from the library
>literally the first paragraph in the book defines infinitesimal work along an infinitesimal piece of curve
>oh so we are in the 18th century
>turns a couple of pages
>delta "functions"
>returns the book to the library

[Anonymous No.9132147]

>>9132138
Physics is mostly a joke, it's your own fault for trying to learn it.

[Anonymous No.9132172]

>>9132147
I initially thought that it's just the beginners' stuff that's mathematical nonsense, because the students didn't have time to learns the maths, but then I was told that it just gets worse and worse.
Can anyone agree or disagree?

[Anonymous No.9132176]

>>9132172
it gets much better. the foundations of quantum mechanics and relativity are mathematically rigorous regardless of how people use them.

[Anonymous No.9132216]

>>9132176
Can someone then recommend some "maths-friendly" books on physics please?

[Anonymous No.9132224]

>>9132172
modern physics is not on firm mathematical footing, but that's because the mathematics hasn't caught up with the experimental results and the successful theories they feed into. mathematicians have quite a long way to go before quantum field theory, quantum gravity, etc will settle in to as elegant mathematical frameworks as do classical physics and early quantum mechanics.

[Anonymous No.9132235]

>>9132216
Takhtajan "Quantum mechanics for mathematicians"
Strocchi "An introduction to the mathematical structure of quantum mechanics"
Slansky "Group theory for unified model building"
Folland "Quantum field theory: A tourist guide for mathematicians"

[Anonymous No.9132280]

>>9132138
>>9132172
If you knew math you would be able to put in the pieces yourself. I understand that it can be tedious how physicists abuse notation and some concepts in textbooks, but it's not that they aren't knowledgeable in the rigorous methods, but they are just too cumbersome for some of the purposes of the book and they recommend some complementary material. With things like virtual work and stuff from lagrange and Hamilton, they are not going to put a whole course in functional analysis in there to properly define what they are because the text is designed to teach the basics to people who may not be than interested in those concepts. It's the same with some shitty intro course in math, you will not see the most general and rigorous structures because the intention is to introduce. Whenever I see "take a diferential element" of something I just think of it as "take a partition and define the Riemann Integral" or "infinitesimals" just something thay ets arbitrarily close to something else which is something I can rigorously define, it's not that hard. The point here is that physics goes beyond math, and you shouldn't read the textbook expecting to sharpen your mathematical skills, but rather, how to formulate and solve problems in physics which is far from trivial.

Though I agree in some cases they act just plainly retarded but that is in University Physics books which I think are a scam. Also, I do agree that even in pretty good textbooks, the way they use vector calc and it's notation is disgusting and confusing, try deriving a proper formula for the electric field of a distribution of charge in terms of line/surface integrals.

[Anonymous No.9132305]

At what point do you know you're not cut out for grad school? Are you supposed to breeze through every class or is struggling allowed?

[Anonymous No.9132308]

>>9132305
It's excruciating except for the 0.01 Percent of the population, but you should be able to mantain an impecable record.

[Anonymous No.9132332]

Couple weeks into calculus 1 now, doing well, already past the chain rule and beyond.

Quotient rule was a joke. Product rule remains my specialty.

I ask my professor his thoughts on quantum mechanics and partial derivatives. He's impressed i know about the subject. We converse after class for some time, sharing mathematical insights; i can keep up.

He tells me of great things ahead like series and laplacians. I tell him i already read about series on wikipedia. He is yet again impressed at my enthusiasm. What a joy it is to have your professor visibly brighten when he learns of your talents.

And now I sit here wondering what it must be like to be a brainlet, unable to engage your professor as an intellectual peer.

All of the deep conversations you people must miss out on because you aren't able to overcome the intellectual IQ barrier that stands in the way of your academic success... it's so sad.
My professor and I know each other on first name basis now, but i call him Dr. out of respect.
And yet here you brainlets sit, probably havent even made eye contact with yours out of fear that they will gauge your brainlet IQ levels.

A true shame, but just know it is because i was born special that i am special. I can't help being a genius, nor can my professor.

Two of a kind is two flocks in a bush.

[Anonymous No.9132357]

Are engineers form a country with non-shit educaton welcome?
>mfw we have calc 1 calc 2 and ode's in one semester

[Anonymous No.9132364]

>>9132332
>takes calc 1 in college
>has the audacity to call others brainlets

[Anonymous No.9132374]

>>9132364
newfag

[Anonymous No.9132376]

>>9132308
You mean straight A's?

[Anonymous No.9132381]

>>9132357
As long as you don't discuss your garbage here. It's the main reason physishits are hated.

[Anonymous No.9132388]

>>9132381
Can I talk about how much I love complex numbers?

[Anonymous No.9132397]

>>9132332

If you didn't complete all your calculus sequence and DE in high school, you're a confirmed brainlet.

[Anonymous No.9132439]

>>9132376
Maybe, the environment is highly competitive.

[Anonymous No.9132441]

Post anime girls solving math problems

[Anonymous No.9132613]

>>9132138
yeah because actual physicists are totally still trying to resolve classical mechanics

[Anonymous No.9132641]

>>9132441

[Anonymous No.9133015]

>>9132613
>actual physicists
Stopped reading right there. I'm not really interested in animals, this isn't a biology thread.

[Anonymous No.9133179]

>>9132388
Yeah. Complex numbers are cool. What do you love about them?

[Anonymous No.9133198]

if i read enough books in math will i become super duper smart?

[Anonymous No.9133200]

>>9133198
>super duper smart
I'm sorry. It's innate.

[Anonymous No.9133201]

>>9133200
but muh flechet spaces!

[Anonymous No.9133206]

>>9133198
No, but you will become better at math. And how much better exactly depends on how smart you are.

[Anonymous No.9133212]

sup, phyics major here

[Anonymous No.9133215]

>>9133212
What happened to the physics generals? I miss them.

[Anonymous No.9133216]

>>9133215
idk but i'm a math student too so i post in both

[Anonymous No.9133218]

>>9133212
Oh... I'm sorry to hear that, anon,

[Anonymous No.9133219]

>>9133206
how much better can i get if i read Basic Mathematics, Geometry Revised, Linear Algebra and its Applicaitons, Stewart Calculus 8e, How to Prove it, ODE by Morris Tenebaum, Discrete Math by Rosen, Naive Set Theory by Paul R. Halmos, A book of Abstract Algebra by CHarles C. Pinter, and Calculus by Spivak? for this year.

Then Algebra by Michael Artin, Analysis I and II by Tao, Principles of ANalysis by Rudin, Linear Algebra by George E. Shilov, Complex analysis by Lars V. Ahlfors, Differential Geometry of Curves and surfaces by Manfredo P. Do Carmo, Geometry by David A. Branan, Topology by James R. Munkres, A classical introduction to modern number theory by Kenneth Ireland, Analysis on Manifolds by Jaames R. Munkres

[Anonymous No.9133222]

Is it true?

> Why more physics can help achieving better mathematics
https://arxiv.org/abs/1708.07735

In this paper, we discuss the question whether a physical "simplification" of a model makes it always easier to study, at least from a mathematical and numerical point of view. To this end, we give different examples showing that these simplifications often lead to worse mathematical properties of the solution to the model. This may affect the existence and uniqueness of solutions as well as their numerical approximability and other qualitative properties. In the first part, we consider examples where the addition of a higher-order term or stochastic noise leads to better mathematical results, whereas in the second part, we focus on examples showing that also nonlocal models can often be seen as physically more exact models as they have a close connection to higher-order modeIs.

[Anonymous No.9133224]

>>9133218
math grad tho omGGG

[Anonymous No.9133230]

>>9133219
You're probably not really interested in all of those subjects. Just pick something you truly like.

[Anonymous No.9133234]

>>9133230
but i am interested in those areas. i don't have one particular area of math i like. if anything, what i'm interested in is how they all connected, like in Deformation Theory. but for that you'd need all those anyway right? it's like Algebraic Geometry with Calculus afaik.

[Anonymous No.9133252]

>>9133222
>History and Overview
Stopped reading right there.

[Anonymous No.9133332]

Tips and tricks for (c)?

[Anonymous No.9133444]

What did they mean by this?

[Anonymous No.9133461]

how can a number be a square? lmao

[Anonymous No.9133470]

>>9130889
>>9131677
Anyone? Please?

[Anonymous No.9133634]

>>9133461
>>>/r/taiwan
>>>/r/dogs

[Anonymous No.9133658]

>>9133332
If R is a field then it only has the trivial ideals: {0} and R itself. The kernel is already an ideal since you're looking at a ring homomorphism. So, what's R/ker(phi)? It should be a field which implies the kernel is maximal. it also implies its prime because a field is an integral domain

[Anonymous No.9133680]

Sup, going to minor in applied math.

[Anonymous No.9133692]

>>9131502
this may be one of the most cringe comments ive ever seen. are you asian???

[Anonymous No.9133775]

>>9133219
You probably won't be able to read all of those in a year, and I suspect you got those specific books from that shitty infographic that's been floating around. Some of them are good, but you need to read them in the proper order, and some of them are just bad.

I should probably get around to making a proper infographic for studying pure math, since there are no good ones at the moment.

For now, go read Smith's "Logic: The Laws of Truth". It's a pretty lengthy book, but it covers basically all the pure logic you'll need to do math. It'll also give you a better perspective on the logic used and notation used when you read other formal texts.

[Anonymous No.9133977]

>>9133775
>pure math
As opposed to "impure math"?

[Anonymous No.9133981]

Is separation of variables the only thing PDE niggers know how to do?

[Anonymous No.9133991]

>>9133977
As opposed to "applied math", obviously, brainlet.

[Anonymous No.9133994]

>>9133991
So as opposed to something which doesn't exist?

[Anonymous No.9134001]

>>9133994
Let's hear your great epiphany about the inexistence of applied math.

[Anonymous No.9134005]

>>9134001
There is nothing to say. It doesn't exist for the same reasons "married bachelors" don't exist.

[Anonymous No.9134008]

>>9134005
>this is your brain after watching a 5 minute video on analytic philosophy
Go read some more kid.

[Anonymous No.9134010]

>>9134008
I couldn't care less about "analytic philosophy", whatever that is.

[Anonymous No.9134019]

>>9134010
So you're even more ignorant than I assumed. Doesn't make the situation any better.

[Anonymous No.9134025]

>>9134019
I'm ignorant about garbage that doesn't interest me. I don't see that as a bad thing since I don't really have that much time on this world to be wasting it on such things.

[Anonymous No.9134031]

>>9134025
>Misuses completely a popular Kantian argument
>I don't want to waste time learning the things I'm trying to use to make my case!!
Yes, that's why you're a brainlet.

[Anonymous No.9134036]

>>9134031
>popular Kantian argument
Couldn't care less as I have already said.
>I don't want to waste time learning the things I'm trying to use to make my case!!
I'm not using anything that needs to be learned to make my case. It's common sense really and any non-retard should be able to intuitively grasp it.
>brainlet
Do you even know what a "brainlet" is?

[Anonymous No.9134040]

>>9133977
>>9133991
>>9133994
>>9134001
>>9134005
>>9134008
>>9134010
>>9134019
>>9134025
>>9134031
>>9134036

[Anonymous No.9134047]

>>9134036
Is "brainlet" like "married bachelor" too?

[Anonymous No.9134048]

>>9134047
No, I'm pretty sure they exist since I'm pretty sure you exist.

[Anonymous No.9134258]

Linear Algebra and its Applications by Lay or Strang? Which better?

[Anonymous No.9134284]

>>9134258
>and its Applications
I don't know, ask in an engineering thread.

[Anonymous No.9134493]

Fucking Chemistry

[Anonymous No.9134553]

>>9132332
7/10, I am impressed that you are able to roleplay a character this narcissistic. Thank you for the giggles.

[Anonymous No.9134565]

>>9134553
3/10 for pretending you fell for a pasta.

[Anonymous No.9134586]

>>9132441
>>/wsr/

[Anonymous No.9134607]

>>9130842
I'm studying physics...

Damn you all Arch-Wizards >.<"


*cri*

:'(

[Anonymous No.9134614]

Today I've succeeded at logarithms and not killing myself yet.

[Anonymous No.9134640]

>>9134607
>I'm studying physics...
>>9133218

[Anonymous No.9134641]

>>9134048
OOOOOOOO!|! ! reeeekktt!!! XDDDDDDDDDDDDDDD!|

[Anonymous No.9134693]

>>9134005
So what about Numeric and Statistic? Isnt that applied math?

[Anonymous No.9134701]

>>9134693
>Isnt that applied math?
Nah, I'm pretty sure they exist.

[Anonymous No.9134715]

>math major entering 3rd year
>average at best student
>still have no clue what I want to do after undergraduate

How do I stop myself from being a total fuckup?

[Anonymous No.9134764]

>2018-1
>still pursuing pure math
>LMAO'ing at your pathetic mathcel lives!
>enjoy your no food or recognition mathfags

[Anonymous No.9134767]

>>9134715
You stop asking /sci/ for advice.

[Anonymous No.9134797]

Why is the diagonal function or even functor called 'diagonal'?

[Anonymous No.9134801]

>>9134797
because if you think of cartesian plane it draws a diagonal line for a graph

[Anonymous No.9134803]

>>9134801
oh, thanks, I am a moron

[Anonymous No.9134816]

>>9134715
>>9134764
Who are you quoting?

[Anonymous No.9134834]

>>9134816
I can never tell if those are newfags or people trolling me.
In the newfag case, the "who are you quoting" line is just too consistent. Then again, it's probably the first thing that would come to mind

[Anonymous No.9134890]

>>9133658
You're thinking along the right lines, but you forget that ker(phi) is not an ideal of R but of R^R, which is not necessarily a field.

[Anonymous No.9135094]

Finding expression for n:th number in a sequence is my weakness. How do you do it. I can sit and stare at sequence for an hour

[Anonymous No.9136290]

>>9134036
>Kant is an analytic

[Anonymous No.9136327]

>>9133230
I truly like Megumin

[Anonymous No.9136352]

>>9130845
>anally annihilated

[sin No.9136530]

>>9130842
Has anyone here dabbled in Computational Linguistics?

I'm a dirty English major, so I've been surprised by how easy I was able to pick up its fundamentals. I have always been shit at math, so I'm pretty proud that I can pick up these discrete math subjects.

Anyone have some good literature for CL?

[Anonymous No.9136539]

>>9134816
>he thinks green text is only used for quoting

[Anonymous No.9136678]

>>9136539
Who are you quoting?

[Anonymous No.9136686]

>>9136678
>"('you')"

[Anonymous No.9136700]

>>9136686
Did you mean to quote a different post? I don't see that text anywhere

[Anonymous No.9137049]

What level of calculus is Spivak? What are the Spivak tier books recommended for algebra and analytical geometry?

[Anonymous No.9137067]

>>9136678

>you are a n!gger

[Anonymous No.9137070]

>>9137067
>you are a n!gger

Why the racism?

[Anonymous No.9137151]

>>9137049
It's "rigorous calculus" level, meaning it's focused in proving theorems in calculus, usually for those who haven't seen proofs before.
For Algebra Pinter's a book of Abstract Algebra is at a similar level. I don't have a geometry recommendation.
If you're new to proofs, my opinion is Analysis I by Terence Tao is the best book out there right now for an introduction to proofs in the setting of calculus. I highly recommend it.

[Anonymous No.9137210]

>>9137070
Because you appear to be subhuman.

[Anonymous No.9137560]

>>9137070
>reddit spacing
>dog-eating
>>>/r/eddit/

[Anonymous No.9137741]

>>9137151
>rigorous calculus
No such thing.

[Anonymous No.9137747]

>>9137741
Just because you went to a school for brainlets with dumbed down calculus classes doesn't mean everyone else did

[Anonymous No.9137750]

>>9137747
It doesn't depend on the school you went to. There isn't such a thing as "rigorous calculus".

[Anonymous No.9137755]

>>9137750
>There isn't such a thing as "rigorous calculus".
see
>>9137747

[Anonymous No.9137784]

>>9137755
see >>9137750

[Anonymous No.9137862]

is it possible to calculate the work done by a 6 dimensional object by taking the integral over the curves traced by the vertices of its shadow?

[Anonymous No.9137985]

>>9137862
>>>/sci/sqt/

[Anonymous No.9138021]

Don't wanna make a new thread, but how does magnitude of vectors differ in 3d planes from 2d planes (if it does at all)

Reason I ask is because this textbook I have says that to calculate the magnitude of a vector, you need to roo the sum of all the components squared e.g sqrt(Ax^2 + Ay^2 + Az^2)

But I don't remember Pythagorean Theorem working for 3D.

[Anonymous No.9138130]

Check my proof please. I need to prove that a group acting freely on a tree is free.

Assume [math]G= <A>[/math] is a group acting freely on a tree [math]T = <V, E>[/math]. Now I want to make this action transitive. Because stabilizer of every [math]v \in V[/math] is a trivial subgroup which means that [math]G/Stab(v) \cong Orb(v) \cong G[/math]. Therefore, all orbits are isomorphic and one may take arbitrary orbit and make group the group act on it. Since orbits were isomorphic such an action will be free as well(and transitive now). So, now group [math]G[/math] acts on a tree [math]T' = <V', E'>[/math] which is a subtree of [math]T[/math]. As group [math]G[/math] is isomorphic to set of vertices[math]V'[/math] I claim that an edge [math](v, w)[/math] exists if there are such [math]g_1, g_2 \in G[/math] and [math]a \in A[/math] such that [math]g_1 a = g_2[/math](an isomorphism maps [math]g_1, g_2[/math] to [math]v[/math] and [math]w[/math] respectively). The fact that there is no nontrivial path from [math]v[/math] to [math]v[/math], for [math]v \in V'[/math] implies [math]g \ne gg_1^{i_1}...g_m^{i_m}[/math] which would mean [math]e \ne g_1^{i_1}...g_m^{i_m}[/math]. Since the choice of group elements and tree vertices was arbitrary the inequality above implies that the set of presentations of [math]G[/math] is empty which makes the group free.

I actually enforced the subtree [math]T'[/math] to be an isomorphic copy of Cayley graph but can I do this?

[Anonymous No.9138229]

>>9131798
This
Generalizing from an experiment implicitly assumes a statistical model of the environment that gives bounds for the accuracy of the estimation obtained from the experiment. In order to predict whether the event will happen after a number of experiments, you have to make assumptions about the space of outcomes and the probabilities of an event happening.

[Anonymous No.9138234]

>>9133332
R^R/ker(phi) is isomorphic to Im(phi) by the first isomorphism theorem. phi is surjective, as for any element of R you can choose a constant function in R^R which phi would send to that element. So Im(phi) = R is a field, and so ker(phi) is a maximal ideal of R^R.

[Anonymous No.9138242]

I think the Babylonian tablet guy's have silently changed their 2-minute promotional video in the past week. Does anyone have a webm saved from that time?

[Anonymous No.9138244]

>>9138242

[Anonymous No.9138513]

>>9138021
Poor brainlet.
It does happen to work think about it.

[Anonymous No.9138521]

Hey I'm dumb, and this is probably not the place, but I've found my books for diff equations, number theory, real analysis, but cannot for the life of me find:
Introduction to Probability and Statistics: Principles and Applications for
Engineering and the Computing Sciences, Milton & Arnold, 4th Ed., McGraw Hill.
Anyone have any ideas? I've scoured libgen/other archives.

[Anonymous No.9139012]

>>9138521
Use your universities library. If they don't have it, you can probably get it with some sort of inter-library loan program.

[Anonymous No.9139042]

>>9138021
It works the same way in 2d and 3d.

[Anonymous No.9139050]

>>9138021
Stare at this picture until you know why it's true.

[Anonymous No.9139064]

>>9138513
Can you explain?

[Anonymous No.9139074]

>>9138513
Ohh, so we are doing pythagorean, but hypotenuse of x and y is just a side for the hypotenuse we want (magnitude), and z^2 is just the other side.
Thanks, smart guy.

Cant visualize it in higher dimensions though.

[Anonymous No.9139080]

Is it possible to learn abstract algebra without prior knowledge of category theory?

[Anonymous No.9139092]

>>9139080
Yes, and that's normally how people learn it the first time.

[Anonymous No.9139095]

>>9139080
Yes, and normally people learn algebra with no category theory. Aluffi's book is an exception in that it introduces algebra and category theory together.

[Anonymous No.9139124]

>>9139012
They didn't, but i'll look into the loan. Thanks

[Anonymous No.9139130]

>>9139080
>Is it possible to learn abstract algebra without prior knowledge of category theory?
No, or at least not properly.

It's similar to how you learn weak approximations to chemistry and physics in high school before doing it in the truly correct language later on in university

[Anonymous No.9139154]

>>9139095
>>9139130
what books do you recommended for category theory?

[Anonymous No.9139176]

>>9139154
>what books do you recommended for category theory?
Mac Lane's book, I don't know why others even exist

[Anonymous No.9139188]

>>9139176
which one?

[Anonymous No.9139192]

>>9137862
Yes, line integrals are trivial to generalize, so you can just calculate it as you do with a 3 dimensional field through a curve embedded in that space just adding more components. Surface íntegrals need more theory and understanding because cross products don't really generalize as you would expect.

[Anonymous No.9139194]

>>9131534
Mind sharing some info on these theorems? Sounds interesting, no lie.

[Anonymous No.9139202]

>>9139176
Awodey

[Anonymous No.9139204]

>>9139154
algebra: chapter 0

[Anonymous No.9139206]

>>9139204
>algebra: chapter 0
Horrible recommendation for category theory

[Anonymous No.9139515]

>>9139130
>>9139206
Ignore this guy >>9139154
. If you're set on learning algebra and category theory at the same time, Aluffi is great. It only makes sense to good deeper into category theory after you've done all the usual undergraduate topics and you feel it matches with what you're interested in.

[Anonymous No.9139528]

>>9139515
>It only makes sense to good deeper into category theory after you've done all the usual undergraduate topics and you feel it matches with what you're interested in.
Wrong.

[Anonymous No.9139550]

Course Description: Linear algebra: vectors, linear transformations and matrices, scalar and vector products, basis and dimension, eigenvectors and eigenvalues, including an introduction to the R scripting language. Single-variable real analysis: sequences and series, limits and continuity, derivatives, inverse functions, power series and Taylor series. Multivariable real analysis and calculus: topology of Euclidean space, limits, continuity, and differentiation in n dimensions, inverse and implicit functions, manifolds, Lagrange multipliers, path integrals, div, grad, and curl. Emphasis on topics that are applicable to fields such as physics, economics, and computer science, but students are also expected to learn how to prove key results.

What does sci think about this class?

[Anonymous No.9139553]

>>9139550
>an introduction to the R scripting language.
seems out of place

[Anonymous No.9139579]

Is all of calculus just trig 2.0?

Does it ever become not-trig? I fucking hate the unit circle. Call me a brainlet I don't care. I've never had any problem with math until this shit. I understand it when it's broken down but theres just so much room for error and everything feels so abstract to me when looking at it as a whole. I have until September 5th to decide if I want to continue with this class or else that's $515 out of my pocket down the drain if I fail it afterward.

Does calc ever become its own thing?

[Anonymous No.9139757]

>>9139579
youre really going to hate the unit square then

[Anonymous No.9139767]

>>9139579
I don't get this meme. My calc course used trig a but in the limit section and in some but not all of my derivative problems.

[Anonymous No.9139770]

>>9139757
This made me laugh anon, thanks

[Anonymous No.9139999]

>>9139767
>I don't get this meme
Fuck off to >>>/r/eddit/ then

[Anonymous No.9140032]

>>9139080
Abstract Algebra was born without category theory. Id say that a better focus for a first course would be gallois theory. I read Rotmann's intro to group theory as my first abstract algebra book.

[Anonymous No.9140047]

>>9139080
Yes, but that doesn't mean you should.

[Anonymous No.9140156]

>>9139154
Awodey's book is probably the best introduction.

[Anonymous No.9140881]

>>9139999
Quads god

[Anonymous No.9140985]

how do i into calculus

[Anonymous No.9141251]

Anyone else find that they use pronouns like "our" and "we" a lot when writing proofs? How much is considered too much?

[Anonymous No.9141269]

>>9141251
If you are going to use pronouns, those are the ones you should be using.