/sci/ - Science & Math

>>10002000
Witnessed!

>>10002004
This all seems so boring. You're a physishit in all but name.

Based Slobodan.

2nd for: French universities are the best in the world.

Maybe I'll finally read that paper on forcing today

>>10002016
Fair, but remember that optimisation isn't just used to solve physical problems, but abstract mathematical problems as well.

To me it's similar to working on AI (in some cases problems are proven to be equivalent), but better because you find algorithms that are actually tractable and not just spamming the same back propogating weight equation on everything.

>>10002027
fifth'd

>>10002059
Don't force yourself.

>>10002059
What paper is it?

>>10002118
>https://arxiv.org/abs/0712.2279
I'm a set theorylet

>csq tu n'est pas francais

>>10002042
Non.

>>10002135
Witty was really smart though

>>10002134
Set theory fag, for me the hardest part to understanding forcing was the machinery one has to put in place for it to work. Don't get me wrong, some forcing arguments are fucking hard, but not CH, cardinal collapse, and other babies first forcing are actually not that bad. Try not to get to bogged down in the details in the beginning.

>tfw third and final year of math bachelor
>tfw less that 30 left out of more than a hundred that started

>>10002217
We tend to forget that the dropout rate for university is colossal. Everyone will constantly tell you that your bachelors degree is nothing to be proud about. But fuck them it's still an achievement in its own right.

>>10002064
I like you anon, I wish you the best.

>>10002217
Name in pic?

Tiens, vu que y'a des Français :
Je suis en école d'ingé privé (je me suis fait mémer assez hard), mais je me suis découvert une passion pour les maths. Je fais du ML en tant que projet, et je pensais bosser un peu dans le privé avant de faire une thèse de ML bien matheuse, peut être a l'étranger (j'ai peut être un plan pour Oxford).
Ca se fait ?

>>10002363
C'est une idée stupide.

I hate this general.

>>10002000
Who's that in the pic?

>>10002321
Belle Delphine

>>10000000

>>10002363
Bof, je m'y connais pas trop en école d'ingé, ni en ML mais pourquoi pas.
Par contre ça risque d'être tendax de choper une thèse vu le nombre de personnes qui se lancent là dedans avec un background un peu plus adapté en ce moment (tout le monde ne fait pas une thèse là dedans, tu me diras, mais quand même).

>>10002363
Go for it. This guy >>10002375 is an idiot.
Machine Learning is very lucrative.

>>10002430
slobodan praljak, a croatian war criminal

>>10002693
To add, he's "notable" because he an hero'd by poisoning himself dramatically in the court room after being convicted of crimes against humanity

>>10000286
Are you the SNS student or someone else who's trying to catfish me with cute anime ?

>>10002693
>Slobodan Praljak
>war criminal

No.

>>10002707
Was his grand daughter the sperm agent behind the consecration of the abomination known as Barron Trump?

>>10002795
>The Lord
Cringe

>>10002693
>>10002707
>>10002739
>>10002795
>>10003161
>>>/pol/

lads
could one successfully major in math if one had both calc aps and a 1540 sat but was a year behind

after reading about people like von neumann or even the fields winner meme i feel intellectually lacking for the field desu

cs meme sounds boring, though

>>10003391
Only brainlets think you have to be a genius to get an undergraduate degree.

>>10003391
>after reading about people like von neumann or even the fields winner meme i feel intellectually lacking for the field desu
The first thing I see when entering this shit general. Leaving immediately.

>>10003529
It's the weekend, of course there are going to be visitors and more off-topic posts. chill out anon

>spend an hour writing proof
>goes to do some chores
>come back and read my earlier writings
>absolutely no idea what the fuck I was talking about

wat do

>>10003718
Post it here so we can alternate between helping you and mocking your incomprehensible proof

>>10003718
try smearing shit on a wall and take a picture of it
math general would be great again

>>10002000
Why is the new Editorial Manager such a piece of shit /mg/?

Fucking can't compile tex for shit.

>do a lot of difficult (for my year level) math during high school due to taking the hardest classes
>get burned out and drop STEM altogether for two years
>now getting motivated to get into math again and maybe work towards getting into grad school for probability or stats
>problem is I haven't practiced for years and forgot some of the basics
If I go to college for a BS in math, am I in for a rough assfucking? Eurofag by the way.

>>10003930
It's easy to get up to speed on something you learned before. You won't really have problems, unless the university you're aiming for is super competitive.

>>10003936
Ok, great. How do I make sure to stay on top of things? It sounds dumb but I never learned how to work hard at school (always got by just by rereading things), so I'm not certain how to deal with university.

>>10003930
Regain back your high school math knowledge, even if it’s mean finishing an elementary book one by one. I recommend George Chrystal Elementary Algebra and Kiselev Geometry. Or start with Apostol on the go. Promise me you work hard, ok?

Recommended books:
http://4chan-science.wikia.com/wiki/Mathematics

You can download math books for free at:
http://libgen.io/

>>10003954
Yeah I bought a book yesterday to refresh my memory. Thanks anon.

>>10003930
You can do it. Don't worry too much about it

>>10003948
>always read (or at least skim) the material before the lectures
>always check the proofs a second time later so that you make sure you understand everything
>if you don't understand something, just go to the professor. don't ask /sci/
>do all the problems assigned in class ASAP
>don't stay up late browsing 4chan or playing video games, even better if you have a set routine of studying from 9 to 17 every day
That's all, there are no secrets to it. Some of it may seem redundant in the beginning, but once you're taking several challenging classes it'll pay off to have good habits. First year at Euro unis are easy, use that to build good habits.

>>10003954
Based anime wikia link poster.

>>10003930
Why do you even want a BS degree to be honest? You can just start a masters in prob/stats and take some supplementary coursework.

>>10002363
t'as aucune chance avec ton ecole de ski privee gros
t'es loin d'etre le seul qui se decouvre une passion pour le ml

>>10004094
ne sois pas méchant

Friendly reminder to report non-English posts

>>10004111
dumb englishposter

>>10004111
>languagelet
mdr

>>>/r9k/48136927

>>10004140
THAT FUCKING SON OF A BITCH TRAITOR

>>10003993
Thanks for the advice.
>>10004038
You can't do that in Europe. I didn't even know you could do a master's without a relevant BS in the US.

>>10004165
>You can't do that in Europe
Wait, do you mean you didn't finish your undergrad? Otherwise you can.

I'm in the EU.

>>10004144
>TRAITOR
I am true to my word m8.

>>10004171
No, I was referring to a BS as in, the degree that comes before the MSc. I'm going to start this year.

Why are weierstrass products so comfy, bros?
>tfw you can create analytic functions with specified zeros

>>10004094
Et une thèse en probas?

Bros, I need help.

Im an EE freshman and to supplement my calc classes (that I don't like that much bc my professor is a meem, nevermind that though) I'm also taking MIT's ocw 18.01.

The thing is that I need to learn proofs and never in my fucking life learnt that, is there a primer on proofs that you would suggest?

>>10004325
If you have the patience for it, study How To Prove It: A structured approach
I used it many years ago and it served me well

>>10004330
I'll look it up, thanks.

>>10002000
Help dudes, this function broke my calculus. a = -1/2 seems to me to be a relative minimum yet Wolfram Alpha says that the derivative at this point exists, and is finite and non-zero. But this contradicts the theorem which states that every relative extremum is a critical point. I think that Wolfram is wrong and that the derivative is not defined at this point, as the two functions inside the maximum are equal in value at this point, but the derivatives have different signs. Pls help a chemist pleb.

>>10004386
You're right. It's not differentiable at -1/2

Im intending to apply to an econ phd. but first i am getting a math bachelor's. If I can only take 2 out of these 3, which should I take? Real analysis, algebra, topology

>>10004426
This is the time when you just let your dick choose for you

Trying to understand tensors.

Suppose I have a vector v <1,2,3> in E3 (ie basis <1,1,1>) and it therefore travels from the origin to point 1,2,3. Now say I change basis to <2,1,1>, but I want to travel between the same points. Is this the "tensor" that does that, ie. is invariant under a change of coordinates?

[math]
\begin{matrix}
1 0 0 \\
0 2 0 \\
0 0 3 \\
\end{bmatrix} [/math]

>>10004447
Trying to understand tensors.

Suppose I have a vector v <1,2,3> in E3 (ie basis <1,1,1>) and it therefore travels from the origin to point 1,2,3. Now say I change basis to <2,1,1>, but I want to travel between the same points. Is this the "tensor" that does that, ie. is invariant under a change of coordinates?
[math]
\begin{bmatrix} 1 0 0 \\ 0 2 0 \\ 0 0 3 \\ \end{bmatrix}[/math]

>>10004448
not the same guy but your question is very confuse me!

>>10004452
If I dot product that tensor by any 3D basis, I should get the same thing right?

>>10003930
focusing on prob and stats is enlightened

>>10004459
i'm sorry, i really can't make out your question
i might not be the one to answer
but i don't know what you mean by dotting a 3D basis; i talk of dotting two vectors/tensors together

>>10002000
I'm starting Calculus I right now and I completely forgot Algebra 2 and Precalculus. I vaguely remember the material and I'm trying to catch up with Khan academy.Should I end it?

>>10004448
Tensors are just multilinear functionals.

>>10004484
If I change basis from i=1, j=1, k=1 to i=2,j=1,k=1 this
[math]
\begin{bmatrix}
1 0 0 \\
0 2 0 \\
0 0 3 \\
\end{bmatrix}[/math]
dotted by <2,1,1> is going to give me a vector that points to the same place?

>>10004473
More like the only way to get a non-research job.

>>10004177
If you have a BA you should be able to get into a MSc.

>>10004502
i must sleep
i still may not know what i'm talking about
but for me, a basis is a set of normalized (norm of 1) vectors
so a basis might be the set of <1, 0, 0>, <0, 1, 0>, <0, 0, 1>, or it might be <cos(t), sin(t), 0>, <-sin(t), cos(t), 0>, <0, 0, 1> for some t
and then one vector, say <1, 0, 0>, i would say is i=1, j=0, k=0
but i can't understand changing basis from i=1, j=1, k=1 to i=2,j=1,k=1 :(

>>10004493
>functionals
>implying tensors map into R ever
Fucking retard

>>10002363
vu ou t'en es oublie la these aux us mdr mais tente les boites de conseil, genre stage de 6 mois et paf ils t'embauchent

>>10003718
Try writing annotations and flushing out your argument more next time you write a proof. My topology prof made us do that for every proof to really hammer in how and why each proof worked so we wouldn't forget the inner workings. It's tedious, but useful. The fact that you forgot the proof so quickly is kind of an indication that there's some gap in understanding.
>>10003930
You'll be fine anon, a math BS isn't as hard as people make it out to be provided you work hard. Make sure to space yourself, you're running a marathon. Each class will build on each other so it's important that you really try and understand the material at each stage. Doing problems will help you get better and math and understand the material. Also there's no shame in going to math stax or whatever to ask about difficulties you're having. Literally everyone who tries out math finds something difficult at some point (unless they quit early), even Tao, Grothendieck, and Scholze all have areas of math that they consider themselves to be weak at. Keep a good pace and also follow >>10003993 advice, it's good. Honestly, 4chan really is a black hole of time and my productivity has gone down ever since I started using the site. Escape while you can.

>>10004503
It's the only interesting application of math desu

>>10004530
You're the retard: https://en.wikipedia.org/wiki/Tensor#As_multilinear_maps

>>10004640
>doesn't understand that the link a special form of the multilinear map under the isomorphism [math]L(V,W) \cong V^*\otimes W[/math] for which [math]V,W[/math] are real and finite dimensional
>calls anyone a retard
Leave your Dunning-Kruger at the door, kid

>>10004638
What is that pic supposed to imply? Stats & prob mostly lead to ML and "data" jobs in industry.

>tfw applied math is almost monopolized by statistics
What are my options if I want to work on real-world problems but stats aren't my thing? inb4 just do physics

>>10004721
Maybe cryptography

>>10004651
The different definitions give the same object when the linear space is finite dimensional.

>>10004750
When the linear space is infinite dimensional there is no way to define 'tensors' and 'tensor products' uniquely, so it makes no sense to talk about unqualified 'tensors' in that case.

>>10004753
What do you mean? The tensor product can still be constructed as a quotient of the free vector space of V × W

>>10004753
>When the linear space is infinite dimensional there is no way to define 'tensors' and 'tensor products' uniquely

Dad went to MIT, your sister went to Harvard, what about you Anon?

>>10004803
Ironic.

>>10004822
I don't know your sources, but they seem to be wrong.

Anon, your half-sister just got accepted into SNS. She even picked up drawing as a hobby! What about you Anon?

>>10004836
Oh crap desu, you're right. I'll fix it up in the next thread or something.

>>10004838
I don't know who you are but I'm not related to any drawings

>>10004842
but are you cute?

No need to explain

>>10004858
I was about to ask whether the that uni is bad but then I realised its acronym is CUNY.

Remember to REPRESENT

What other Uni are you Anons in?
Asking for a friend

>>10004905
>What other Uni are you Anons in?
U of T

>>10004905

>>10004921
lmao

Not gonna do the discount Lyon

>>10004905
lmao, my uni is ranked 351-400 by QS. I won't humiliate myself further by naming it.

>>10004912
Srry, took a while desu

>>10004905
None.

>>10004942
>Srry, took a while desu
I meant U of Toronto :(

>>10004977

>>10004987
based

>>10004987
nice, looking like a rotman thot

>>10004987
You could do something important with your time, too. Just saying.

>>10004997
>You could do something important with your time, too.
but she is

>>10005001
How is he doing anything important?

>>10005004
I actually just finished reviewing for my calc 2 & chem exam that's supposed to come in 2 weeks so I'm just taking a break doing this desu

>>10005019
Oh wow! That's an incredible feat!

>>10005022
kek

>>10004935
Why are the grandes ecole so popular on /mg/ now

>>10005039
Because France is the only nation that is good at math

>>10005043
But do you get 300k/starting

>>10005054
Americucks only care about hard cold cash and not the prestige

>>10005043
What do you base that on?
Is that observable even at the licence/bachelor's level?
t. frog

>>10005062
They are barbarians. Instead of embarking on an intellectual journey, they desire money. To reach this money, they behave like the moslems shouting "Allahu akbar" by praying for Jesus to help them.

I never knew cute anime girls and university logos actually work together. Cute girls really make anything work huh.

>>10004987
Source of original art please.

>>10005084
Heading off to work rn, if this thread is still alive I’ll drop the sauce or someone else can

>>10005086
I only need the name of the artist.

>>10005087
Sorry anon I don’t really look at the names of illustrators.

>>10005065
I base it of this
T. Unwashed barbarian of the north

>>10005019
>ETH Zurich isn't aligned to the paper.

Anooooon

>>10005019
>I actually just finished reviewing for my calc 2 & chem exam
Stay out of the /mathematics/ general, please.

>>10005039
It was about time

>>10004905

>>10005300
Stop larping
The idea that so many anons in this particular general would come from the most elite french schools being unlikely is an understatement

>>10005305

>>10005323
God I want to kill myself

>>10004905
best argie eng uni
tfw brainlet though.

How do you guys find time to do other shit? Like I used to do math as a hobby, but also enjoyed reading, especially the classics. Now however once I've started studying it in a relatively good uni, my time is gone. It's not too bad, about 40 hrs a week is the expected study time, but this leaves basically just the weekend. I'm afraid I'll burn out if I force myself to study other stuff "for fun" in my free time.

>>10005382
I've wondered about that as well, but I think probably we should just quit 4chan forever

>>10004905
based rutgers
>went to this school because i did badly in hs and its not too competitive
>major in math and find out its actually got a really good math department

>>10005199
I was hoping no one realized it cuz I spent a little bit too much time doing others and not enough time on eth (rush to get dressed for work)

Quick rundown on the difference between multivariable calculus, vector calculus and calculus on manifolds? I vaguely guess manifolds are more general than vectors but I'm really lost on this.

>>10005300
Bitch I did that one already.
(Nice ass uni tho, respect)

>>10005305
You would be surprised. A lot of anons here actually came from top tier unis

>>10005323
Fuck. So there really are normaliens here too? Now I really wish that fag posted his email address in previous thread.

>>10004937
Unless you're in detroit or bagdad, then no one will remember it.

There used to be a time when only losers were posting on 4chan you know. What are all these successful people doing here?

>>10005531
There’s 1-2 from ENS and 1 from SNS

>>10005531
I wanna bang the SNS one

>>10005540
>the probability that a future Fields medalist is posting here is not entirely negligible
>mfw

>>10005382
From this day forward I will do nothing but math 24/7. I will do math in my sleep! You think all these fuckers who go to fancy schools have me beat? No way, I do not give up and I never back down. Fuck all of you.

>>10005540
What are they working on?

>>10005562
Urethra insertion.

>>10004937
You too fuckhead. Don't let these snobs with sticks up their asses bring you down.

>>10004942
You too. Hit the books.

>>10004931
You too. We Gattaca now!

>>10004899
You too. By pure force of will alone, we will shit all over these babies who were born with a coin in their mouths!

>>10004858
You too. It's time to cut all the Harvard/MIT/SNS/EPFL/EP/ENS faggots down a notch.

>>10004987
Not you though. Leafs get the rake.

Is this what an existential crisis feels like?
What have I been doing with my life?

I am never posting on 4chan again. Everything went downhill with Trump. God I fucking hate 2016. This site should have always been an obscure indonesian basket weaving forum.

>cluster point
>accumulation point
>adherent point
>limit point
>condensation point
>sometimes used interchangeably, sometimes some are special types of others, some are used only when studying metric spaces, some are used only when studying the real line

WHY ARE TOPOLOGISTS SO FUCKING AUTISTIC

Hey guys, hopefully someone can help

I'm struggling really badly in real analysis 1. The problem I have is I have abslutely no idea how to start manipulating expressions and equations to get to the desired result. Does anyone have advice regarding that? Should I start with the desired result and work backward?

For example: A simple case.

Prove n^2 > n+1 for n>=2 by induction

I know to start with n=2. That's easy

And I know I must show that (n+1)^2 > (n+1)+1. But I don't know how to get that. Is this supposed to be the easy part? Or is it supposed to be hard?

>>10005718
You want to deduce the thing you are trying to prove from the induction hypothesis.
You know that n^2 > n+1
You want to show that (n+1)^2 > (n+1)+1
Is there some way of manipulating this so that terms from the thing you know appear in it? (hint: try expanding)

>>10005718
It doesn't really matter which way you work. A good strategy can sometimes be to manipulate both sides and try meet in the middle. In this case I think it's easier to work backwards from what you are trying to prove though.

>>10005728
this is it, use induction hypothesis

Is this readable?

Also I feel this proof could've been a lot shorter

so in signals, if you have P_inf then E_inf must also be true right?
P = power, E = Energy

>>10005766
go ask the engineers

>>10005718
This: >>10005734

Manipulate both sides, see what you can get from it. Sometimes you can actually go full backwards because of propositions being equivalent. Example: Trying to prove that if n > 1, then 2n > n+1.

Sometimes you cant't go completely backwards. For instance, in your problem, if you work backwards you may get to the inequality "n(n+1) > 1", which is obviously not equivalent to the proposition "n is a natural number". But, starting from the assumption that "n is a natural number", you can get to the inequality "n(n+1) > 1", and what you have done here is manipulating and meeting "both sides".

This method of problem solving is highly used even in more "advanced" mathematical courses, and is a fundamental tool in mathematical thinking (most proofs from elementary set theory can be tried this way for example).

For more info on what I and other anons are trying to explain check out How to Prove It by Velleman.

>>10005758
Guess you're asking for redaction, but fix that spacing on god

>>10005770
haha n1 meme now answer my question

>>10005758
Maybe explain at the top that you're breaking into those cases and why they cover everything?
I've never done graph theory so it might be super obvious and not necessary.

version 2

I'm not sure if I have to prove basic combinatorics such as the pigeonhole principle in detail here

any recommendation for a more practical approach to lineal algebra? not that i don't understand shit like axler, but i'm in a memengineering course and i don't think studying theoretical stuff will help me in the finals.

why are shifts in discrete and continuous different?

>>10004386
d/da limit from left = 0
d/da limit from right = 0

function is smooth and continuous

>>10005841
It depends on the shifting value. It is implied in the figures that no is positive and t0 is negative

>>10005850
oh t_0 < 0 so t - t_0 would be t + |t_0|

Test

>>10005531
I used to be in an ENS too, I went to X for my PhD

>>10005711
Because you have to be precise, which leads to all types of terminology (adherent point <> limit point <> cluster point). All of these make sense for metric spaces.
Now for the reason why there are redundancies, I am guessing that some people calqued directly from french (eg accumulation point) and others used a more anglo terminology (eg. cluster point). This or the french translated the terms and it became a standard even in the anglo saxon world

>>10005597
>you will never study at a top uni
>you will forever be mediocre

I greatly enjoy watching more old-school math documentaries like the following:

https://www.youtube.com/watch?v=ObPg3ki9GOI (The Birth of Calculus).

Generally speaking something calmer and having more insight than most modern American "documentaries".
Is there something like a playlist or a website with videos like the one I linked or with math lectures more accessible to a layman?

>>10004810
i had sex with onee san and gave her the shot
now she carries my seed

>>10005382

>>10005382
>>10006590
I basically don't.
I swim 3 times a week and try to rockclimb a bit too but that's a struggle. I don't read at all during the semester. I read genre fiction trash before exams to help relax sometimes but I do all my serious reading in the breaks. I'm a member of a few uni clubs but I generally only attend the first few weeks of a semester.
One thing I do do is watch a bit of french youtube which doesn't feel particularly strenuous but helps me improve my understanding of the language.

>>10004426
skip topology

What's with the "Lang is a meme" meme?

Could someone perhaps help out with these questions? Cheers.

You have $250,000 for investment. There are 2 securities A and B. You invest 40% in security A and the remaining in security B. The standard deviation of security A is 0.60 while the standard deviation of security B is 0.60. The correlation between the returns on the 2 securities is -0.70. What is the variance of returns of the portfolio?

Question 3 Unsaved
When correlation coefficient between returns on securities j and market returns = -0.60; standard deviation of returns on securities j =14.60% and standard deviation of market returns = 13.60%. What is the beta value of security j ?

To raise $980,000, a company draws up a bill of exchange with a face value of $1,000,000, payable in 170 days. What is the implicit annual market interest rate on the bill?

Question 5 Unsaved
An investor has $1,000,000 to invest. Out of this $1,000,000, she invests $100,000 in asset A, $200,000 in asset B and the remaining in asset C. The beta of asset A is -0.6, the beta of asset B is 0.6 and the beta of asset C is 1.1. What is the beta of the portfolio?

ABC Ltd is currently paying a dividend of $3 per share. If investors expect this dividend to be maintained forever and require a rate of return of 7 percent on the investment. What is the value of each ABC share today?

>>10006716
It's baseless propaganda by Rudincucks, Alfohrscucks, Artincucks, etc.

>>10006730
What have you tried? These all should be straight forward from the definitions. Go back to your notes and look at the definitions of the things you are asked to provide.
>Reminder: /sci/ is for discussing topics pertaining to science and mathematics, not for helping you with your homework

>>10006749
>Rudincucks
Rudin is a meme too.

>>10006760
So who's an example of a good author?

>>10006765
>So who's an example of a good author?
Riehl

>>10006768
>Riehl
Made for rape.

>>10006768
I was reading her category theory in context the other day because someone here mentioned it. Doesn't seem too bad desu

Is this book any good for learning real analysis?
https://www.amazon.com/Calculus-Complete-Course-Robert-Adams/dp/0134154363

>>10006779
>her
Riehl identifies as a "him".

>>10006781
Proofs?

>>10006777
God will it.

>>10006780
>Is this book any good for learning real analysis?
Why don't you read it and find out?

>>10006790
Because I'm hoping someone with more experience can save me effort down a bad path,
and because I think it looks like a silly book to learn real analysis from given that it's *very much* a calculus book.

How do I prove it doesn't matter whether or not I have an open or closed interval in the definition of zero content?

>>10006818
>How do I prove it doesn't matter whether or not I have an open or closed interval in the definition of zero content?
define "zero content"

any recent research on the category of axioms?

>>10006820
Let [math]A\subseteq \mathbb{R}[/math]. [math]A[/math] is said to have zero content if for all [math]\epsilon > 0 [/math] there exists a finie collection of closed intervals, [math]I_{1}, \dots , I_{n}[/math] such that: [math]\displaystyle A \subseteq \bigcup_{n=1}^{N} I_{n} [/math]
and [math]\displaystyle \sum_{i=1}^{N} | I_{n} | < \epsilon [/math].

The sad thing about studying math is that youll never have that "yo let's cook" moment even after you got a phd in maths and spent 4 weeks looking for the best rope. Your dog looks at you with his starved eyes and most you can manage is yo lets multiply these 2 really big numbers and after that rape someone. Really takes a toll on you

>>10006856
Nice projections.

>>10006856
>The sad thing about studying math is that youll never have that "yo let's cook" moment even after you got a phd in maths and spent 4 weeks looking for the best rope. Your dog looks at you with his starved eyes and most you can manage is yo lets multiply these 2 really big numbers and after that rape someone. Really takes a toll on you

>>10006853
The second condition should hold true regardless of the interval, but the first condition I'm not sure. It seems like it should 'just work' but I can't formalize it.

>>10006853
Go through the definition and think about what happens to the complement.

>>10006874
>>10006853
Assume the definition with closed intervals holds. You are given epsilon. Take a closed covering such that the total length of the covering is less than epsilon/2. Then substitute each closed interval with an open interval which contains the original closed interval and whose length is bigger by epsilon/2n. You obtain an open covering with length less than epsilon. The other direction is trivial.

>>10006926
Thanks

>>10006958
no prob buddy

>>10006784
LOL

>non-constructive mathematics

any good books about calculus?

I have the following problem about matrices:
Let [math]A[/math] and [math]B[/math] be matrices such that [math]AB = BA = 0[/math]. If [math]A + B[/math] is invertible, is [math]A - B[/math] invertible?
I can't find any counterexamples, mostly because I find it hard to find such matrices. I am inclined to believe it is true because if [math]A[/math] is [math]2*2[/math] and idempotent and [math]B = I - A[/math], [math]A - B[/math] is invertible.
But I have no idea how to prove it. Any pointers?

>>10006368

anybody?

>>10007060

>>10007118
calm down ping ling, i wont steal your 300k job

>>10007110
Hint: Consider (A + B)^2 and (A - B)^2

>>10002027
>2nd for: French universities are the best in the world.
Why not German?

>>10006985
How exactly do you "substitute" the closed for open?

>take real analysis course
>instructor does zero teaching
>homework presentations everyday where students basically teach the class

just kill me boys, any tips on self studying real analysis

>>10007231
That problem is trivial. Just treat the partial sequences as cauchy sequences and show there is only one per equivalence class. Contradiction should work, assume 2 distinct are in the same class but there exists an epsilon which separates the sequences. Use absolute value metric.

>>10007133
>Consider (A + B)^2 and (A - B)^2
How did you come up with that, holy shit.

[math](A + B)^2 = (A - B)^2 \quad \Rightarrow \quad [det(A + B)]^2 = [det(A - B)]^2 [/math]
From this we can conclude that:
[math]det(A - B) = det(A + B) \neq 0 \qquad \vee \qquad det(A - B) = -det(A + B) \neq 0 [/math]
In both cases, the determinant of [math]A - B[/math] is not zero, so the matrix is invertible

Is that a good proof or do you think that there is a better way to do it?

>>10007271
I'm not the anon who suggested, but it is very natural. You have a product formula on an algebra which has a sum and product and you want to make a statement about sums. So cosider multiplying the sums to see if your given product appears. This is more of a general algebraic technique than matrices in particular.

I'm supposed to generate a prime p such that p-1 doesn't factor into a product of small primes. Could you guys help me ?

>>10007285
You don't.

>>10005572
Based and redpilled.

>>10005613
Cry more söygöy.

>>10007271
What >>10007279 said.
Your proof is good enough but you could also find the inverse of A - B in terms of the inverse of A + B by multiplying both sides of your first equation by the square of (A + B)^(-1). The advantage of this solution is that it's completely algebraic, so it holds even if A and B are from an arbitrary ring.

Why is it so filled with french mathfags, are they even french or richfags from other 3rd world countries that couldn't get into american universities?

They certainly look like a loud minority.

>>10007308
Why ?

It seems clear to me that if you have Riemann integrability on a closed bounded interval, when increase the number of points in a partition, [math]L(f,P) \leq L(f,Q) \leq L(f,Q^{*}) \leq \cdots \leq L(f) \leq U(f) \leq \cdots \leq U(f,Q^{*}), U(f,Q), U(f,P)[/math], for partition and refinements [math]P, Q, Q^{*}[/math], etc, but how do I formalize this in context of the [math]\epsilon[/math]-criteria for integration: [math]U(f,P)-L(f,P) < \epsilon[/math] for [math]\epsilon >0 [/math].

>>10007369
meant to put this in /sqt/, but oh well have at it if you want.

How does one show that \left (\mathbb{N}, < ) is pairwise non-isomorphic with \left (\mathbb{Z}, < )

>>10007388
>How does one show that \left (\mathbb{N}, < ) is pairwise non-isomorphic with \left (\mathbb{Z}, < )

>>10007388
N has a least element, Z does not (also pairwise is kind of silly when there is only one pair)

>>10006856
Is that a Breaking Bad reference ? What are you complaining about exactly ?

>>10007421
I guess I'm having trouble formally constructing a proof given the definition of an isomorphism as S: v -> f(v).

How do I state this more formally? I'm also trying to prove this for (Q, <) and (N, <) -- forgot to remove the pairwise. Once I know how to do it for one, I was going to follow the same steps.

>>10007436
Find a set in Z or Q that does not have a least element.

>>10007436
Well assume that there were indeed an isomorphism f: N -> Z. Then, f(1) is the least element of Z. Indeed, if n is in Z, then there is an n' in N such that f(n') = n. Then, since 1 <= n', we must have f(1) <= f(n') = n, hence n >= f(1). Hence f(1) <= f(1) - 1, a contradiction.
Basically, what you must understand is that saying that two structures are isomorphic means that they are essentially the same (ie. any property that is preserved by morphisms must be shared by the two structure).
Similarly, you can find a property of the order on Q that is not shared with Z or N, which implies that it cannot be isomorphic to either (by an argument that resembles the above).

>>10002739
Based. Only beta cucks disagree

>>10004668
The pic is implying that the retard on the left will never even begin to comprehend what "machine learning" actually is.

>>10007285
2

>>10007369
For all epsilon > 0 there exists partitions such that blah blah blah

How do I deal with not being intelligent in a nonlethal way? My sixteen year old sister is probably smarter than me. I wish I weren't a brainlet.

>>10002693
based and redpilled

How easy is it to get a CS/programming job with a math undergrad degree? Is it worth double majoring in CS just to secure jobs?

>>10007542
samefag and I'm gonna say yes, and not to take advice from competitive strangers on the internet

good luck you handsome devil you

>>10007537
i hate you

>>10006368
I like this one for the personal story it tells, quite romantic
https://www.dailymotion.com/video/x1btavd
https://www.youtube.com/watch?v=Y7Ufxl-zSRI
Same with
While not really what people think of as a documentary I still like showing this to people, it's usually enjoyable for everyone.
https://www.youtube.com/watch?v=U_ZHsk0-eF0
>>10005382
I experimented until I found the best time of day, location, and method for studying, at least for me. I go to the library early in the morning after exercising and eating. Regular exercise will help you immensely actually, at least it did for me, same with changing your diet. It's really fucking obvious hindsight. I read a few articles and books that really helped me learn what my "style" was when it came to studying and doing math as well.
>>10006780
People shit on Rudin but I like it. Tao is good, same with Simon for his early chapters. I've heard good things about Rosenlicht and Pugh. Jost book was nice as a second course, maybe it could be used as a first course.
>>10007060
https://en.wikipedia.org/wiki/Calculus_Made_Easy

>>10007524
Yes, but what kind of partition.

>>10006368
>>10007564
You what, I'm gonna modify my answer, if you wanna learn about the really cool stories or mathematics and mathematicians then you're better looking for various texts and articles rather than documentaries. Here's an example
https://www.ams.org/notices/200503/fea-weil.pdf

>>10007333
The language of mathematics has been French since Descartes anon. For the last 500 years most great mathematicians have been French with the occasional German, Englishman and Russian thrown in.

>>10007566
>but what kind of partition
The explicit form of the partition depends on the function mate. Have you never done any analysis proofs at all?

>>10004905

>>10005783
Strang(le yourself)

>>10006832
still no definite answer on what the morphisms are

>>10007285
every number is either a prime or a factor of small primes or 1. So if p-1 doesn't factor into a product of small primes, then it must be prime or 1. If the former, then p must be 3, if the latter, it must be 2.

>>10007452
This is great, thank you.

>>10007834
104723 - 1 = 2 * 52361

>>10007916
retard

>>10004514
While it's common practice, and while it helps with computation, a basis does not have to be normalized in general. All a basis is is a set of linearly independent vectors that span the space. The traditional {i, j, k} = {<1, 0, 0>, <0, 1, 0>, <0, 0, 1}>} is a basis for R_3 because no vector in the basis is a linear combination of the others, and every vector in R_3 can be written as a linear combination of these vectors, i.e. v = a_1 * i + a_2 * j + a_3 * k for any v in R_3. However, this also means the modified basis anon gave, {i*, j, k} where i* = <2, 0, 0> and j and k are the same is also a basis. i* is a constant times i, so it should be pretty clear from a contradiction argument that i* cannot be written as a linear combination of j and k. At the same time, any vector in R_3 can be written as a linear combination of this modified basis, constructively from the coefficients a_1, a_2, a_3 for v in the {i, j, k} basis, as v = a*_1 * i* + a_2 * j + a_3 * k = (a_1 / 2) * i* + a_2 * j + a_3 * k for any v in R_3.

All that being said, all that noise anon was saying about dotting bases and tensors is garbage, and indicates a fundamental misunderstanding of the subject.

Logic Question:

given some model, M, and some sentence, s, and a is an M-assignment, then how can I show that if M ⊨ s[a] then M ⊨ s[a] for all truth-assignments/evaluations, a?

Seems to be induction on terms/formulas by the definition of assignments, but unclear on the base case. Any insight?

>>10005382
There are 168 hours in a week. If you get 6 hours of sleep a night and spend about 3 hours on busy work (eating, self care, cleaning), that's still over 100 hours to yourself. If 40 hours of studying leaves you with "just the weekend," you're doing something wrong.

>>10004905
Any Melbourne kids here?

>>10007285
Download any cryptography library for your favorite programming language. The cardinalities of any finite groups used for DH, RSA, ECC, will be such numbers.

>>10004905
Not the best international ranking, but I do enjoy it here

>>10008099
I know a bunch of people at Melbourne.
Is it true you guys only have one algebra course?

>>10004753
It can be identified by its universal property..... So yes it's unique.

>>10005510
Idk but in my school vector is well vectors. Multivar is tensors (and some representation theory for some reason) and manifolds is well manifolds. So vectors really just are matrices and shit. Multivar is learn what tensors are and look at general linear mappings/modules etc. Manifolds is define the exterior product/exterior derivative get to the integral form and greens theorem (tangentbundles etc too).

>>10008178
It appears so, but I'm a second year, so I wouldn't know

Anyone have Wolfram pro? Can you type this in and tell me if it gives an answer. I know the answers are ~-151 and~91, but I want to see if Wolfram comes up with something exact.

solve for x: 2*5*7577/77/77-ln(77-74)+2ln(77)-ln(74+77)=tanh^2(5x/77+atanh(74/77))+2*ln(cosh(5x/77+atanh(74/77)))

You know when people say ‘Marco’ you say ‘Polo’? It’s like that but with ‘Probability Theory’ and ‘Fun’.

TEH WHITE

Hello. What's the best functional analysis book to learn from after I learn higher level real analysis (so measure theory, etc)? All the better if it treats variational calculus.

>tfw I thought I was a hopeless dummy in my honors analysis class but it actually turns out everyone just copies people's answers from MO and the solution manual while I try hours to find elegant solutions

Will I be ok?

>>10004905
UofT
>>10004912
What year?

>tfw I can't grasp the difference between a N-dimensional array and a tensor

>>10008704
They are isomorphic. A matrix is a representation of a linear transformation.

>>10002000
sometimes I look in these threads, but since I'm doing combinatorics it feels like I don't really have much in common with the topological/algebraic oriented population. does this reflect the actual hierarchy in mathematics?

>>10008738
Combinatorists are more or less shunned since what they find interesting about certain objects (say, Banach spaces) is not what people studying those objects (functional analysists in this case) find interesting.

>>10008718
Is this the same meaning as "the matrix of an endomorphism is isometric"?

>>10008772
No?

>>10008829
Tensors might be as far as my brain can go :(

>>10008277
I'm in second year and doing algebra 3 (algebraic number theory).
Which courses are you doing at Melbourne?

>>10008704
There is none

>>10004905

If I want to prove the Riemann Hypothesis, which areas of mathematics should I focus on? Analytic Number Theory and Complex Analysis?

>>10009189
The Riemann hypothesis has been scrutinized enough that's its likely the result will come from a field that hasn't been developed yet.

>trying to read paper
>it's an illegible low-quality scan
If my department had the funding I'd pay undergrads to retypeset these in latex

>>10009304
Do it yourself and become a modern day manuscript-preserving monk.

I have my qual today. Send me your energy, /mg/.

>>10009358
you're gonna make it anon

>>10009358
Good luck.

>>10009189
Algebraic Geometry

I'm currently finishing and engineering undergrad and to be honest I don't like it, I just enjoyed the math courses I took. So, obviously, my knowledge of math doesn't go beyond fourier analysis and vectorial calculus. Is it possible for me to continue studying math ?

>>10009189
mathematical physics

disk method theorist

>>10009431
Have you done any proofs-based classes?

>be in first year of math at low tier eurofag university
>want to get into an MSc program at a good/great university
>afraid good grades aren't going to cut it when the name recognition of my university is almost nonexistent
Should I try to transfer out next year? When should I start talking to advisors about master's programs?

>>10009612
I am at a top 150 math program, so good but not great. (Physics dept at my school is top 50, a lot of mathfags work with them.) A lot of people here come from engineering background or physics. Also a lot of people come from no name places. I would say it like this:
Your work is more important than your school, but a big name school has more opportunities for interesting work. It is still possible to get in somewhere good, but some people have an advantage.

>>10009479
No, I haven't taken that courses

>>10009449
>tfw too brainlet for rigorous disk method theory

I don't understand the notation of this equation:
(x, y, z) = 1
Further down there's also (u, v) = 1.

>>10009812
I think it's supposed to be the gcd of these numbers.

>>10009830
cheers, that makes sense

>>10004905
Already finished my degrees

Okay guys i have no idea about:
>e, logarothmic, sinus / cosinus functions
>have never done anything with vectors / matrix
>Never had any physics classes

and i'm going to study applied math and physics in a couple of weeks, how fucked am i? I've always wanted to get into cosmology / astronomy or anything related to research, which is why i decided to study these fields, but i'm already scared to death by the upcomming analysis 1&2 and linear algebra classes. Are they going to be hard for someone like me?

Pic related are going to be my classes in the upcomming first and second semester

>>10009285
I want an objective answer, motherfucker.
>>10009409
>>10009433
I don't get sarcasm, so are you guys being serious or just sarcastic towards me?

>>10010077
There isn't an objective answer you brainlet, if people had any fucking idea how to prove RH it would have been done by now

>>10010084
But it must related to some field of mathematics, I just wanna know which field that is. From what I know about the RH, it's related to Complex Analysis and Analytic Number Theory.

Do you guys buy the Pajeet (International) Edition of all your textbooks?

Or do you believe in supporting our publishers?

>>10010088
Its related fields are all just a subset of Computer Science

>>10010281
>buying

>>10010035
>Are they going to be hard for someone like me?
You're going to stumble, you'll be okay if you're a generally smart person. The concepts aren't that tough to grasp.

>>10010281
>buying hundred dollar textbooks while I'm a half-ass broke student with 50k loan

>>10010565
Those are shitty books.

>>10010565
Link to that.

>>10007803
are you doing masters? if so, how are things there?

Anyone know the name for the pattern formed in base 10 when you multiply by a prime number, and the last digit of the product follows a cycle of fixed size? Like 0 - 3 - 6 - 9 - 2 - 5 - 8 - 1 - 4 - 7 - 0 - 3 - 6 - 9 for 3, and 0 - 5 - 0 - 5 - 0 for 5, or 0 - 2 - 4 - 6 - 8 - 0 - 2 - 4 for 2. I'm going to fuck around with it in higher bases with bigger primes and see what I get, but I wanted to know if there is more information about it first.

>>10011852
Interesting question.

>>10010088
It is a statement that can be phrased in terms of analytic number theory, but as with most "real-life" problems (especially unsolved ones...), it cannot be pinned down to one particular field (not to mention that the mere notion of "field of mathematics" becomes increasingly vague as you learn more about math).
It has been studied extensively from various points of view: analytic number theory, algebraic geometry, noncommutative geometry, mathematical physics, etc.

>>10010281
>supporting our publishers
>supporting
>publishers
The whole industry ought to be destroyed desu. Nonprofit book publisher when?

>>10009189
You might want to take a look at random matrix theory, there is hope that we might me able to tackle the Riemann Hypothesis using tools from RMT

>>10012015
I forgot to said this but look at the Hilber-Polya conjecture

>>10010565
That library is too big to be useful.
>Books on X subject plox!
>Here are 50 pdfs with just the title and author!
At the minimum I'd advice maintaining a second folder of "checked out" books and copying the PDFs you're currently reading into it. It will help keep that shit from becoming overwhelming. Though you're honestly better off looking for books as you need them and grabbing them off libgen.

>>10011985
There's also self-publishing setups like Lulu. Though aside from HoTT and Basic Analysis you won't find much good stuff on Lulu.

>>10009409
based
>>10009433
cringe

>>10011571
I'm about to start my PhD there actually, haven't started so no clue. Looks nice

>>10004325
Introduction to Mathematical Thinking on Coursera teaches the very basics.

>>10011852
Modular arithmetic.

Because carries propagate from right to left, the units (rightmost) digit of the output is only affected by the units digit of the input, the tens digit of the output by the units and tens digits of the inputs, etc. So any fixed number of rightmost digits will form a cycle. Multiplying by a number coprime to the modulus always forms a maximal-length cycle.

In base 10, any prime other than 2 or 5 is coprime to any power of 10, so the last digit will follow a cycle of length 10, the last two digits a cycle of length 100, etc.

>>10009304
>>10009325
CS undergrad here. You idiots can't into OCR?

>>10012302
Even CS can't into OCR. I tutor a CS course and we had to manually sort 400+ signed anti-plagiarism pledges instead of just indexing them by OCR.

>>10012302
It actually has been but the pdf is still presented as a scanned image, I imagine because it would be impossible to recreate the formatting.

>>10012302
>>>/g/

>>10012488
>>10012488
>>10012488