/mg/ - Math general

No physishits edition.

What are you studying, /mg/?

Other urls found in this thread:

s3.amazonaws.com/aops-cdn.artofproblemsolving.com/products/aops-vol1/toc.pdf
s3.amazonaws.com/aops-cdn.artofproblemsolving.com/products/aops-vol2/toc.pdf
libgen.io/search.php?req=9781934124109&open=0&res=25&view=simple&phrase=1&column=series
s3.amazonaws.com/aops-cdn.artofproblemsolving.com/products/intro-counting/toc.pdf
arxiv.org/abs/1708.07735
twitter.com/AnonBabble

i'm teaching calc 2 this smester hbu?

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

Generatingfunctionology, good book

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
s3.amazonaws.com/aops-cdn.artofproblemsolving.com/products/aops-vol1/toc.pdf

>Vol. 2
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.

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

>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.

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

Unitl you accept it.

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.

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?

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.

>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

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

>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.

Here's the list of contents for that book:
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.

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

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.

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

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?

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

are physicists even real people

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

At least 500

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?

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

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.

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.

fusion categories + potential relationship with quantum symmetry groups

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"""

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

What's wrong with apple math?

There's nothing wrong with fiction. But there's for that.

He's an edgy high schooler

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

>applied mathematics
begone redditor

>Lol no.

back to your physics containment thread, physiplop.
>

Why is Veeky Forums 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.

Can someone point me to literature about subobject classifiers?

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

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

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?

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

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

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.

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"

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.

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?

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

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.

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

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

newfag

You mean straight A's?

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

Can I talk about how much I love complex numbers?

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

Maybe, the environment is highly competitive.

Post anime girls solving math problems

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

...

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

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

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

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

but muh flechet spaces!

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

sup, phyics major here

What happened to the physics generals? I miss them.

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

Oh... I'm sorry to hear that, user,

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

Is it true?

> Why more physics can help achieving better mathematics
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.

math grad tho omGGG

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

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.

>History and Overview
Stopped reading right there.

Tips and tricks for (c)?

What did they mean by this?

how can a number be a square? lmao

Anyone? Please?

...

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

Sup, going to minor in applied math.

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

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.

>pure math
As opposed to "impure math"?

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

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

So as opposed to something which doesn't exist?

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

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

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

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

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

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.

>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.

>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?

...

Is "brainlet" like "married bachelor" too?