/sci/ - Science & Math

Bump.

>>10261835
dont retard. The best outcome is that you enjoy a class you didnt need to take, most likely you'll end up lowering ur gpa when you fail the class. just study analysis by urself

Do lots of problems, take your time. Expect to spend 2-3 times more time on this course than other math courses.

There are not many definitions to learn in real analysis, the hard part is in doing many problems and learning all the little tricks to do proofs..

>>10262186

I won't lower my GPA if I fail. It's outside of my transcript. Also, I would like a certificate (as I may get one).

>>10262194

Triangle inequality, multiply by 1, add 0. That's what I've heard.

>>10261835
>a summer course on real analysis
I doubt any math majors will be going, and if they do, laugh at them for being freshmen.
People overestimate real analysis a lot. It's essentially a combination of really easy proofs, five hours of trivial algebra for inequalities, and random solutions to sequences.

>>10262186
don't economists need analysis to go to grad school?

Also oeconomics is for grills

>>10262768
Oeconomics for faggots.
This post was made by chrematistics gang.

>>10262768
Yes, they do.

Mathfags, how much time do you guys usually take to solve for one analysis exercise?

OP here and I'm taking like more than 2 hours to solve one exercise about limit of sequences.

>>10262990
Like 2 minutes, unless it's an evaluation or inequality.
Post it.

>>10261835
So your the favela monkey that keeps shitting on america education. Go suck a fat dick fart monkey

>>10261835
I think Cauchy looks like Putin

>>10263007

Here it is.

Prove that for all $p \in \mathbb{N}$, we have $\lim_{n \rightarrow \infty} \sqrt[n+p]{n} = 1$

>>10263020

Fuck off, it's my first time posting here.

Most uni's in Brazil (including IMPA, the one I suspect you're attending this summer) adopt a topology influenced book so some familiarity (the introductory chapter will suffice) with the subject could help (look for Topology by K. Jänich or Elementos da Topologia Geral, E. L. Lima).
O Elon tem duas séries de análise, geralmente o IMPA usa o "elon fino", cilada. Corre atrás do "elon grosso"(vermelho), é mais amigável. O capítulo mais importante é o de introdução a topologia, se você compreender ele o resto é trivial.

>>10263025
[math]1<=n^{1/(n+p)}<=(n+p)^{1/(n+p)}[/math].
We set i=n+p, and the problem is [math]i^{1/i}[/math] converges to 1 when i goes to infinity.
You should be able to figure yourself out from here.

>>10263033

I'm not going at IMPA, I didn't had my scholarship approved there. Going to Rio paying all for myself is expensive as hell.

I'm using the smallest one, Análise Real, vol. 1. I thought Curso de Análise was for whole semester courses.
Thanks for the tip, but I guess now is too late. My course begins at 7 January.
I will at least read the introductory chapter of Elon's Elementos de Topologia Geral then.

>>10263048

>to IMPA

Fixed.

>>10263033
>>10263048
IMPA is the best graduate program in Brazil?

>>10263189
For maths? Yeah, definitely.

>>10263189
Not him but yes.
I confirm as another Brazilian.

Latin America's only field medal winner Artur Avila did PhD there on Impa.

I'm an undergrad in UFRJ (Rio de Janeiro Federal University), the Uni that Artur Avila did his Bachelors.

The best Math Grad programs in Brazil are
# 1. Impa # 2. USP # 3. UFRJ

>>10263216
>>10263220
What about PUC-Rio?

>>10263220
The problem with USP is that their bachelor's curriculum is strangely goofy.
>>10263223
>being brazillian
>paying for uni
Ayyyyy lmao.

>>10263225
I guess most math undergrads at PUC-Rio have scholarships.
Also, I was asking about their graduate program.

>>10263230
I'd imagine it's bad since everyone good is going to IMPA or UFRJ.

>>10263220

You forgot to say that Avila did his Bachelors at UFRJ at the same time he was working towards his PhD at IMPA. I guess it was merely a formality to get his PhD degree.

>>10262194
>There are not many definitions to learn in real analysis, the hard part is in doing many problems and learning all the little tricks to do proofs..
>not being expected to be able to prove 100+ major theorems and lemmas by heart during the orals

>>10263034
another anon, cant we also say, as n goes to infinity, n+p would be bounded by n thus making (n)^(1/(n+p)) = n^(1/n) = 1?

just curious

>>10263223
Puc-RIo is 3rd best in Rio de Janeiro City behind Impa & UFRJ


According to Brazil's "Folha" University Ranking
>which list Undergraduate programs rather than Graduate &changes every year

#1 UFRJ #2 USP # 3. Unicamp #4 UFMG #5 UNB #6 UFGRS #7 UFSCAR #8 UNESP #9 Puc-Rio #10 UFSC #11 UFPR
>http://ruf.folha.uol.com.br/2018/ranking-de-cursos/matematica/

#12 and below are meme tier

It doesn't list Impa since Impa isn't a Uni

Impa is #0 since it's better than any Uni in the list

>>10263258
You sure can. Nice solution, anon.
The thing with sequences is just going full schizo and coming up with a bound. Sometimes, the bound takes five pages to write, in which case we give up and wait for Euler to do it for us.
>>10263261
MOTHERFUCKING UFSC REPRESENT

>>10263261

How can Unesp be "better" than PUC-Rio? I'm from there and don't like this uni at all.

>>10263258

This looks so obvious. I feel like a brainlet.

>>10263272
Even the good math courses in Brazil are bad by international standards. It's a mix of "we can't make all the cotistas drop out" and "niggas come to us knowing literally nothing what the fuck".
What we do have is a solid basis in Euclidean geometry courtesy of vestiba, which honestly justifies a lot.

>>10263220
>>10263261

Is it worth going to UFRJ for an Applied Math undergrad degree?

I will already have a degree in Economics, so it's kind of shitty going for another undegraduate major, another 4 years.

>>10263276
it happens anon. from personal experience, never do math on the fly, always think on it for a bit first.

>>10261835
>Any tips for an Econ major

Never write about sex.

*REEs in SWERF noises*

>>10263369

OP here. I want to get as far way as possible from Economics.

>>10263645

>away

Fix'd.

>>10263645
>wanting to get far from literally the best science
Anon, come on.

>>10263660

Economics is indeed the most successful of the applied social sciences. Microeconomics is developed and robust than whatever sociology bullshit. However, I'm more interested in statistics and new techniques.

>>10263660 >>10263881

Economics has too much political bias bullshit.
Ranging from Radical Marxism to Radical Anarcho Capitalism.
Radical Ideologies that mess up with a country's economy instead of helping.

Statistics & Financial Math are more reliable.
Statistics has its own issues too though as unreliable, biased or fabricated data for example.

The best ideological approach should be a moderate & pragmatic balance between free market & less regulations combined with a healthy & moderate state incentives on education & public infrastructure. And Combat against corruption.
Unfortunately Economists and Policy Makers tend to be ideological rather than pragmatic.

>>10264033

It's even worse here in Brazil. A lot of political bullshit propaganda at public universities. Very crazy stuff.

Thank God there are some few good schools though.

>>10264033
Nice critique about the teaching of economics.
Where did you get your PhD?

learn how to write really neat epsilons

>>10264083
Not him, but he's right.
t. uni was QS-ranked no.123 when my PhD was conferred.

>>10263033
>O Elon tem duas séries de análise, geralmente o IMPA usa o "elon fino", cilada. Corre atrás do "elon grosso"(vermelho), é mais amigável.
holy fuckeroni I've been studying from pic related this whole time without realizing it's not my course's book. that must be why I'm acing it

By the way, how good is an IMPA MSc/PhD for someone interested in algebra (I'm thinking representation theory)? I get the impression that their forte is more the analysis/topological side of things, but then again it's pretty much the Latin American Mecca for mathematics we're talking here

>>10264423
Why would the smallest book, used during the summer, be the hardest?

Should it be like an introduction?

>>10261835
Definitely learn about mathematical proofs if you haven't already. Read Hammack's Book of Proof.

>>10264442
I think anon meant that "Elon fino" is more amiable than "Elon grosso". Fino is about 191 pages long and (my edition of) grosso is 344. The latter covers many more topics that one would expect from a second course in analysis and maybe even later courses (right now I'm reading the last chapter in function sequences and series and it mentions equicontinuity and some comments on power series in [math]\mathbb{C}[/math])

>>10264461

Oh, ok. So I continue with the fino but also read the introduction of grosso's?

>>10264476
Comparing both, I'd say the "fino" (Análise Real) is just the "grosso" (Curso de Análise) with some things shaved off. The structure is the same and even the same paragraphs are used in most places. If the course you're taking is of an introductory level, you'll be fine with the fino. (my math department uses that text for Calc I.) If you have already taken a proofs-based Calculus and wish to delve further into the subject, go with the grosso.

>>10265020
>my math department uses that text for Calc I.
Holy fuck, are you the anon from UFRJ?

>>10263034
is the $$i^{1/i}$$ convergence to 1 something that's trivial to prove, or is that something most analysis students already know? it seems obvious once I look at it, but it would not appear in my mind unless a hint specified it

>>10265474
You just apply the definition of a power (that is, [math]i^{1/i}=e^{\frac{log i}{i}}[/math] and use L'hospital to show that the power goes to zero.

>>10265484

Why would you use L'Hôpital? You haven't been introduced to derivatives yet.

>>10265423
No, I'm from Chile. Attending one of the top universities here

>>10265515

why are you using real numbers? you haven't been introduced to dedekind cuts yet

>>10265515
Tbh you can prove that (log i)/i coverges to zero without using L'Hospital, it's just worse. You have to do stuff like set log(i÷j)/(i÷j) and exploit log properties, which kinda sucks.
Alternatively, you can show that for any rational x>1 there's p such that x^p>p, which does the job too. This one's pretty trivial. Use the binomial expansion, pick the big term in it, and beat the shit out of it until it coughs up the inequality while shooting the smallest p that works over by a couple millions.
L'Hospital is just extremely convenient.
>>10265968
Best definition desu.