/sci/ - Science & Math

[Anonymous No.4510682]

I don't think there's anything I hate more in the world than Real Analysis. What in the fucking shit. It seriously needs to get raped and die. This shit is just retarded, comes out of absolutely fucking nowhere, there is no logical means to solve the problems unless you know the "tricks" to them by either the professor telling you in class or magic, and everything we do is COMPLETELY FUCKING POINTLESS. We all know calculus works who the fuck gives a shit about this stuff.

If you like this bullshit you are everything wrong with the world. Abstract Algebra is where it's at. Now that's a real math class. Fuck this gay fucking Analysis bullshit FUCK.

[Anonymous No.4510686]

[Anonymous No.4510689]

>not sure if troll or silly mad teenager

[Anonymous No.4510691]

I agree, real analysis is the most anal part of math and algebra is just so much better that it's not even funny. Worst part is that almost all the mathematicans at my university are analysts, so most advanced courses are on "interesting" and "fun" subjects like special kinds of functionspaces and detail studies of convergence issues.

[Anonymous No.4510690]

>>4510682

NEVER DO THEORY MATH
NEVER DO THEORY SCIENCES
THIS IS THE YEAR 2012

DO APPLIED MATH, APPLIED SCIENCES, ENGINEERING, FINANCE AND YOU WONT HAVE TO WORRY ABOUT THIS POINTLESS MENTAL MASTURBATION

/THREAD

[Anonymous No.4510693]

Enlighten me as to what is 'real' analysis..

[Anonymous No.4510702]

>>4510690
Theory math in abstract algebra is actually useful though. You can use the permutation groups to solve a Rubik's cube and you can figure out the rotations of polygons and shit.

Calculus is cool and all and it's good to know all that stuff, but spending ages and ages doing these retarded USELESS proofs of shit that clearly works already is just so so so lame. And to make it worse these proofs are completely non-intuitive and difficult as fuck on top of already not giving a shit.

[Anonymous No.4510707]

>>4510693
It's analysis where the base field are the Reals, of course. The other usually nicer analysis would be complex analysis, working with complex numbers.

[Anonymous No.4510709]

>>4510707
lol, you guys hate THAT?
That's so basic it's funny

[Anonymous No.4510711]

>>4510707
what's complex analysis like? is it the same misery and pain of real analysis but with complex numbers? or any different?

[Anonymous No.4510712]

>there is no logical means to solve the problems
>unless you know the "tricks" to them by either the
>professor telling you in class or magic

>you hate proofs


LOL

[Anonymous No.4510715]

>>4510711
seriously dude: WHAT is the pain and misery in analysis?

[Anonymous No.4510716]

>>4510709
its not exactly basic; its not calculus if thats what you thought. We are talking measure theory, topology, and proving stupid stuff using "clever" estimates to no end.

[Anonymous No.4510717]

>>4510702
>useful
>solving rubik's cube
lol

[Anonymous No.4510718]

>>4510712
I like proofs in Abstract or Linear Algebra. In those classes if you knew the material well you could logically deduce what was going on and come up with some clever manipulations of the concepts to get to make a proof.

But in Analysis it's like you just go "hurr how bout let f(x)=blahblahblah by MAGIC and epsilon=random shit out of nowhere, then poof! theorem proved"

[Anonymous No.4510720]

>>4510711
It's generally slightly better but once you get into more complicated stuff then yeah, same shit, same misery.

[Anonymous No.4510722]

>not sure if troll or engineer
well done, either way

[Anonymous No.4510724]

>>4510722
I'm in my 2nd year bachelor civil engineering and calculus isn't that hard so don't talk smack

[Anonymous No.4510727]

>>4510724
Calculus = babby arithmetic (just follow da rules)
Real Analysis = proofs galore (and not babby delta-epsilon either lol)
No comparison man, no comparison...

[Anonymous No.4510728]

>>4510718
Well, to not be a dick: I don't like proofs that much either, but the truth is it isn't magic and it isn't hard. Complex things are just a lot of easy things at once, so study hard and you'll get throught it champ

[Anonymous No.4510729]

>>4510727
Dude Analyse is dutch for Calculus.
I'm PRETTY sure it's the same thing..

[Anonymous No.4510731]

people who think it makes no sense haven't tried enough to understand, I was in this position before, then I entered graduate school and started questioning the foundations, then bit by bit things start to make sense... it's only done so that we can be sure that what we are doing is correct mathematics, not just guesses

complaining won't get you anywhere (good)

[Anonymous No.4510734]

>>4510724
Civil is fucking easy. I majored in structural only because it was the easiest and fastest to finish.

[Anonymous No.4510735]

>>4510729

[Anonymous No.4510737]

the truth is they could just skip most of it and go straight to topology and metric spaces, it's the same definitions but written more intuitively (using the metric function)

[Anonymous No.4510739]

>>4510729
Oh, so the words in Dutch are the same! That clearly carries a lot of meaning when we are discussing things in English!

Look at this book and tell me you covered that in calculus class: http://dangtuanhiep.files.wordpress.com/2008/09/principles_of_mathematical_analysis_walter_rudin.pdf

[Anonymous No.4510740]

>>4510731
The real problem is that the didactic methods used are usually completely inappropriate to the subject. The undergraduate course at my school felt really scattershot, just a bunch of disjointed proofs of admittedly important theorems sort of cobbled together. In Algebra it feels much more like a solid narrative of structure being built from the ground up, same with Topology. In fact, now that I've gotten through my first half semester in Topology I'm only now starting to see what was really supposed to be going on in Real Analysis. If the standard method started with Topology from the ground up and worked through to metric spaces and then Analysis, it would feel more coherent and less hand-wave-y I think.

[Anonymous No.4510741]

>>4510739

Thanks.

[Anonymous No.4510743]

>>4510739
YES.
Actually ALL OFF IT.
ask me anything about it faggot, I'm serious.

[Anonymous No.4510747]

>>4510740
yeah, it feels to me that real analysis requires too much mathematical maturity compared to the other courses

[Anonymous No.4510750]

>>4510743
I am dead serious.
I had ONE course ONE semester called CALCULUS in my FIRST year of college and I understand ALL those concepts.

Don't run away bitch, ask me anything

[Anonymous No.4510751]

>>4510750
university*

[Anonymous No.4510752]

>>4510743

>Obviously you went through all of the book.
And no, you didn't go through that in calculus class.

[Anonymous No.4510753]

>>4510718
The fact is that these proofs you're looking at have been rewritten many times in order to make them look so pretty. The first time through, you're supposed to do a lot of grunt work and figure out what f(x) and epsilon are, then you go back and rewrite it as though they were obvious from the start. So don't feel to bad that you're not able to pull them out of a hat, the ones writing the proof didn't either.

[Anonymous No.4510755]

>>4510750
Sure. Prove Godel's incompleteness theorem. You have 5 minutes. GO!

[Anonymous No.4510758]

>>4510747
Not so much that it requires more maturity as that it has a lot of background that's usually glossed over or ignored inappropriately. You wouldn't try and teach Galois Theory without thoroughly going through Field Theory first and expect it to feel right, nor should you ignore the foundations of Analysis when teaching it.

[Anonymous No.4510759]

>>4510755
I study proofs on my short term memory, I could easily look that up and ctrl+V that here, but I won't.

You can believe me or not, but we had to study one +- 1200 page book called: a complete guide thought calculus and it had everything in it what I can read in this books index. That the truth.

[Anonymous No.4510763]

(completely underelated it was a way better book too)

[Anonymous No.4510767]

>>4510750

I'll bite.

Prove open and closed intervals in R are connected. Not even a bad one.

[Anonymous No.4510770]

>>4510759
Okay, give an outline of the proof for the Heine-Borel Theorem (a set is compact iff it is closed and bounded). That's certainly relevant to the material of the book, not too complicated, and probably not explicitly proved there.

[Anonymous No.4510771]

>>4510718
>But in Analysis it's like you just go "hurr how bout let f(x)=blahblahblah by MAGIC and epsilon=random shit out of nowhere, then poof! theorem proved"
You're supposed to work backwards to find out what epsilon has to be on scratch paper, and then write out the proof choosing that "magic" value of epsilon.

[Anonymous No.4510774]

>>4510767
Suppose [0, 1] is not connected. Then [0, 1] = A ∪ B for two nonempty sets A, B such that A ∩ B =
A ∩ B = ∅. Suppose, without loss of generality, that 0 ∈ A and 1 ∈ B. Let
x = sup A.
Since A ⊂ [0, 1] is contained in a closed set, x ∈ [0, 1]. Now certainly x ∈ A, for otherwise x could not
be a least upper bound for A. Hence x /∈ B, since A ∩ B = ∅, so x ∈ A, since x ∈ A ∪ B, thus x /∈ B,
since A ∩ B = ∅. Hence there exists a neighborhood U ⊂ [0, 1] of x disjoint from B. Thus U ⊂ A.
Since 1 ∈ B and x /∈ B, x < 1. But then any neighborhood within [0, 1] of x contains points greater
than x, hence some y ∈ U ⊂ A is such that y > x. This contradicts the construction of x as the least
upper bound for A, and we conclude that [0, 1] is connected.

also read
>>4510759

[Anonymous No.4510776]

>>4510755
This isn't analysis and isn't really that hard either - the concept is inventive, but the proof itself wouldn't be much more enlightening. More analysis-ey questions:
-Show that closed intervals in the real line are compact.
-Summarize the construction of the real numbers from the rationals.
-What is the definition of the reimann integral?

[Anonymous No.4510778]

Can't we just agree that Leuven is a better university then whatever shitcollege you went to and call it a day?

[Anonymous No.4510782]

>>4510776
>What is the definition of the reimann integral?

that's just insulting

[Anonymous No.4510785]

>>4510782
Its simple and isn't something someone who just studied "calculus" would know.
>>4510774
>Now certainly x ∈ A, for otherwise x could not
be a least upper bound for A
what?

[Anonymous No.4510786]

>>4510774

There's a less convoluted way to proof, but you did answer. I still can't believe that you learned all of this in 1 calc course. Even if with a 1200 pager. What uni?

[Anonymous No.4510787]

>>4510786
Leuven (Belgium)

[Anonymous No.4510789]

>>4510787

Well that makes it easier to believe. I was assuming some ameri uni. lol

[Anonymous No.4510791]

>>4510785
You did have the basic idea right btw (although awkwardly phrased), its just that line that is wrong. You have to say that maybe x is in B, in which case the neighborhood of B contains a point y < x, in which case y is also an upper bound for A, contradicting the fact that x is the supremum.

[Anonymous No.4510792]

>>4510787
It was a very good book thought. I will look it up for anyone interested as it was in english. Just a moment..

[Anonymous No.4510797]

>>4510792

rlderms there

[Anonymous No.4510800]

srry, had the name wrong

[Anonymous No.4510806]

>>4510797

uhuh. Don't know how the verification got onto my comment.

[Anonymous No.4510807]

it's this
<==

[Anonymous No.4511300]

Posting this again because people should just listen to this man.

http://terrytao.wordpress.com/career-advice/there%E2%80%99s-more-to-mathematics-than-rigour-and-proo
fs/

Patience and discipline. You lack them.