/sci/ - Science & Math

Pleb, you're doing it wrong

always wear your yellow sweatshirt

Very funny meme picture. Thank you, OP.

le upboat

Depends on the context. On a non-babby level of math I would agree.

Depends on the person.

But... Sometimes it can seem easy if someone has already solved it and is giving you a slow but thorough explanation.

>>5841167
Why would you solve something again someone else has already solved?

I would say the opposite is true. If it doesn't seem easy, you haven't learned it properly.

>>5842745
Einstein would agree.

Huh, on exams, I always found the opposite to be true.

In real life it's true though. If it is too easy, you're not going to get any grant.

I find that the opposite in most exams

If the answer doesn't come out as a nice log or surd or whatever then it's probably wrong.

Define 'easy'.

Some people think difficult = tedious, I prefer to think that difficult = conceptually challenging.

Doing 37 integrations of trig functions multiplied together is tedious, not difficult. Learning why you're doing those integrations 37 times and determining the limits would potentially be more difficult.

>>5838658
I've made so many mistakes because some part of me thinks that's true.

>>5843144
I eventually learned to stop believing this. But fuck if I didn't miss out on A's because of this.

Gauss said that if Euler's Identity was not immediately apparent to a student upon being told it, that student would never be a first-class mathematician.

So who am I going to listen to, some faggot OP, or one the finest mathematicians in history saying that if mathematics isn't intuitive and easy for you, you're fucked?

>>5843185

you're retarded

euler's identity usually gets taught before you learn series, which is necessary to understand the identity

>>5843197
>He has to be taught what it means to understand what it means
3rd-rate mathematician detected.

>>5843185

I'll just point out that just because Gauss said that, doesn't make it any more true.
Also:
>saying that if mathematics isn't intuitive and easy
That's not what Gauss said.

>>5843185
Mind you Gauss was a genius and you are not. You are definitely appealing to authority here, which is a logical fallacy. Mathematics doesn't come intuitive to everyone. I sucked at math throughout highs school. Literally got D's. Couldn't do it. And I graduated a year ago with a degree in math and finance w/ 3.9gpa. So, no, I'm didn't listen to a Gauss, I didn't have to. I'm good at math and I know it. Even if I didn't understand Euler's identity at first. Even if I did get bad grades. So I say fuck Euler, anyone can be a mathematician.

>>5843212

It's not that anyone can't become a mathematician. It's that not everyone can become a Guass.

>>5843212
>I'm good at math and I know it

What's the highest level of math you learned?

>>5843212
>>5843225
Please don't start a pissing contest guys

>>5843219
Galois was smarter than Gauss anyway.

>>5843229
>no fun allowed

>>5843212
>I'm good at math and I know it.

>>5843225
I study at Boston University right now for my MA. And I don't know what you mean by highest. If you are asking what is the most difficult for me then I'm going to say it was a topics class on vector bundles. Still pulled through it though. Another one that was difficult for me because there was so much stuff to keep track of at once was a course on advanced stats and stochastic processes. But what was hard for me doesn't mean it was hard for everyone. Some people just went through that topics class like a hot knife through butter. You meet amazing people who you know you'll never beat, and I just have to learn not to sweat it.

what drives a man/woman to get a tattoo/this kind of self injury?

>>5843271
Drugs and/or Alcohol?

>>5843271
>That zero

It looks like an untidy ring of bacon

>>5843244
>tfw know all my times tables up to 100

Suck it. I'm good at math.

>>5843271

A misguided attempt to fit in and seem "deep"

>>5843271
Edginess.

>>5842982
>Huge complex equation
>Simplify it
>It comes out as cos(x)
>Not sure if utterly wrong or very elegant question

>>5843324
Yeah I get that, I had an integral involving arsinhx and some other crap and when I did a substitution it all came down to the integral of u. I was surprised but it definitely worked.

Here, I'll try to LaTeX it because it was a very nice question.

<div class="math">\int_0^1 \frac{1}{1+x^2} sinhx dx</div>

>>5843349
Shoot, that should be

<div class="math">\int_0^1 \left\frac{1}{1+x^2} arsinhx\right dx</div>

>>5843355
Bloody hell

<div class="math">\int_0^1 \left(\frac{1}{1+x^2} arsinhx\right) dx</div>

>>5843212
>anyone can be a mathematican
>I say fuck Euler
>Graduated with a degree in finance and maths
>Probably at a community college

I like to see you try and develop research in combintorical graph theory you fucking idiot. Pissing around with rules and forumlae dosen't make you "good" at math, what separates the faggots from the men is how second nature math is to you.

>>5843252
What did you learn about vector bundles?

>>5843358
pi/4*arcsinh(1)-2?
very fun problem, was good review to derive all of the differentiation formulas for arcsinhx

>>5844640
Care to elaborate on how you arrived at that, good sir? I'm struggling. It'd be trivial(ish) if the 1+x^2 were square-rooted...


Also, Wolfram doesn't like doing it exactly, but does give a decimal approximation of 0.32617

http://www.wolframalpha.com/input/?i=int+%281%2F%281%2Bx%5E2%29%29arcsinhx+dx+x%3D0..1

However, that's not the same as your answer of -1.3 ish...

Not the person you asked, but if I'm correct, the solution is:
-i Li_2(-u)+i Li_2(u)+arctg(x)(arcsinh(x)-ln(1-u)+ln(1+u)) + C, where u is ie^(iarctanx) and Li_2 is polylog function

>>5842745
this

>>5844640
>>5844697
Aha, guys I made a mistake in writing it out

the 1+x^2 part should all be square rooted, embarrassing

It should be a lot nicer now.

>>5844783
yes you are correct I made a mistake last night...

>>5844783
>wolfram alpha

>>5843236
Where did you find Galois' IQ?

>>5846718
Who said anything about IQs?

>that face when you always overlook minute shit and it always throws off your answer even though you have the mechanics down

The one thing I hate about math education is that the teachers love to give exercise that give a nice round answer. We're conditioned to think if our answers are ugly there's a mistake somewhere.

Uh, no?

Rule of Math (And engineering, and sciences in general)

If your answer is more than 3-5 lines, you are doing it wrong.

>>5842745
>you haven't learned it properly.
Whilst I want to agree, high school math is taught in the same way bible classes are taught: memorise shitloads and rote learn the entire thing. Learning what the concepts mean? Nah, don't do that, waste of time, we have 8 variants of the same problem to memorise patterned answers to.

Now maths in CE, that's when if it seems easy, you're doing it right. DSP stuff only seems complex the first time you look at it, it's also not a thing you can really do confidently without "getting" it.

>>5843271
I never got this equation.

What's the significance of it? You might as well have tatoo'ed cos(0) - 1 = 0, it's about as meaningful from what I understand.

No need for arbitrary rules.

Saw that Zorn's lemma, Stokes' theorem, Hilbert's Nullstellensatz, Riesz's integral representation theorem or Brouwer degree in nonlinear analysis in undergrad? Did you try proving them yourself without looking at the proof? No? Then why are you learning maths? Switch to accounting or physics.

If you find them easy, you're not doing it wrong. Just do whatever you like. If learning maths does not make you humble, you don't need to be.

>>5846819

lol, dsp is barely math

babby mode Routh–Hurwitz stability

>>5846812
You havent take differentional equation eyt doesnt?

Stay pleb you first year newbie

>>5846824
>lol, dsp is barely math
It is. It's just not purely theoretical, like what you're used to. It actually has useful applications and can solve real life problems (as all engineering), so it's lolnotmaths.

>>5846822

That only links 2 fundamental constants, not quite as cool as five.

>>5846849
cos(pi) - i*sin(pi) + 1 = 0

Can I win a prize?

lol that would hurt putting on someone's back.

>>5846854
The relation between exp and cos, sin is not present in yours.

>>5846854

Firstly, no e. Secondly, pi is used twice, which is less elegant. Thirdly, i is only included by cancelling it out with multiplication by zero, which hardly counts.

exp[pi*sqrt(164)] = Large Natural Number
173 odd which can be written in 2 ways

>>5846823
How do you prove Zorn's lemma?

>>5848346
What's yellow and equivalent to the Axiom of Choice?

>>5846750
You claimed Galois was smarter than Gauss.

>>5848969
You didn't answer my question and that was someone else.

>>5846812
>If your answer is more than 3-5 lines, you are doing it wrong.
If you answer can be written in 3-5 lines you are probably doing it wrong/ in high school.

For a babby-tier example, I'd be impressed with someone setting up and solving a transportation problem with a primal-dual algorithm where the initial solution isn't optimal in less than a page.

>>5843212
No, everybody can be like you, force feed yourself math until it makes sense. That's not a mathematician, that's a monkey with a calculator. Have you discovered a new, complex theorem and proved it? That's what Gauss was thinking about when saying "mathematician".

>TFW when for an instance you forgot that you had to FOIL and just distributed the exponent, so you wrote it out, but you caught yourself, but now you're pretty sure that the TAs are laughing at you when they grade this

>>5849170
>the hilarious moment when your calc lecturer suggests that people are copying each other's weekly assigments and that it was obvious because so many people used (x+y)^2 = x^2+y^2
I'm pretty sure it was case of engineers gon' engineeer, though.

>>5848793
Zorn's lemon. ;)

>>5848998
My last post should have. Intelligence/"smartness" is measured by administering an IQ test.

>>5851227
Then I agree.

>>5850401
Where am I able to buy those? I could not find any at the market.

I really think it would benefit students who do more than the absolutely most basic math requirements in college to have exposure to rigorous proofs. After I took a class on writing proofs, I realized that most "math" you're taught up to that point was "Here's this rule, here's this procedure, follow these steps and you get the answer."

Fast forward to the differential equations class I enrolled in for muh graduation requirements. Most of the class is engineers, who are always complaining about how "merth es so herd." I'm not trying to start a math/engineer circle jerk or anything, but I really think that if they had gone through proofs, they'd realize all they're doing is regurgitating algorithms. And it would simply seem easier in comparison.

all these people raging at the op, because they never push their limits, like their comfort zone, and easy achievements. cowards, cowards, all of you.

>>5853690

Maybe the engineers need more philosophy requirements.

>>5853770

I don't push my mental limits because it retriggers childhood trauma and I shut down.

>>5843271
>not getting a math tattoo

>>5853770
>all these people raging at the op
Where are you getting this?

Windows 7 sucks

>>5853804
I am baffled

>>5853805
I understand

>>5853804
This thread is not about windows 7 and I think your picture is inappropriate.

>>5843022
>doing 37 in series/combination and getting every operation correct
>no mathematica
>no calculator
>low time limit
>implying this isn't hard as fuck if you are doing taylor series tier shit or higher

>>5853804
windows 8 sucks

>>5843271
e^iPi=-1
e^2iPi =1
i=0
Nigga wut?
IMAGINARY AZZ MATH FUK DIS SHIT BRUH

>>5854940
>taylor series
>hard
confirmed for underage

>>5843294
>tfw i dont know like any times tables

Actually, one of the first and most important lessons you'll learn in an actual math course ("actual math" meaning a proof-based theory course and not the applied turn-the-crank garbage they teach to undergrads in hard science) is the ability to discern when the answer to "is that it?" is "yes," and to know that often, many things are no more complicated than they appear.

Getting hung up on simple shit is the best way to be terrible at math. Guaranteed.

>>5853791
Why would you get that tatto?

This is kind of accurate for me, especially back in highschool
>Acing all my math classes
>ACT comes around and I'm feeling so confident
>Start the math section
>"Holy shit this is easy"
>Get through it in 30 minutes
>Get scores back
>A 24
>mfw
At least I got a 33 in Science and a 28 overall

The solution to any problem should be the simplest, and easiest solution to implement that you can possibly conceive of. If your solution isn't simple you should find a better solution until you can't simplify it any further.

>>5843185
In a sense, Gauss was wrong: it is not necessarily true that the definition of the natural exponential function for real numbers be the same as the definition of the exponential function for complex numbers, just as long as the complex definition corresponds to the real definition when the argument is real. It could be defined, for example, that the complex exponential corresponds to the real exponential for real arguments, but is identically 1 for all other arguments in the complex plane.
This is all to say that that the definition of the exponential for complex arguments is the same as the definition for real arguments is not a theorem, it's, well, a definition. And definitions are of course contingent.
There are, however, many reasons why we define the exponential in such a way, but most of them are in a way historical: because of the way we have defined objects or done mathematics in the past, it's the only convenient option.
In the seventeenth and early nineteenth centuries, when all this was being discussed, mathematicians did not realize that the definition could be different. That's where they, and Gauss, were wrong.

>>5855258
This so much. I know some people that get hung up on the dumbest things so much so that they miss the entire POINT of the problem. Shit's frustrating to try and help.

"Alright, so I started it off with let epsilon greater than zero be given"
"k"
"or is it consider all epsilon greater than zero"
"uhh...okay, whatever that's fine"
"but I mean, which was is it?"
"either one is fine, go on"
"Okay, consider epsilon bigger than zero...wait...is it bigger? or greater than? is bigger okay?"
"uhh..."

Shit like this all...the...fucking...time.

This is a real one:
"Problem A: prove that if f is defined on a rectangle R and property_______ holds, then f is integrable.
Problem B: using problem A and (property that can be shown to be a special case of property ______) show f on R is integrable

But problem A says "defined on" and problem B doesn't how can we use problem A I don't get this blah blah blah we don't know it's defined on"

Relax. It tells you to use problem A. It sounds very similar. Freaking out about minute irrelevant details isn't helping you understand the theory.

>>5855313

This is likely because high school math curriculum teaches Magic Formulas, not math.

>>5846819
This is true and it makes me sad...

One of the main reasons I'm still debating if I want to go to college or not... I've learned so much more and so much better whilst studying by myself... my last 3 years of school didnt teach me shit because I became passionate with what I was studying and therefore was 50 steps ahead of everyone...

Why is the school system aimed at retards nowadays?

>>5838658
The converse is true, if it seems hard you're probably doing it wrongly.

>>5855419
Are you saying calculus isn't hard math?

>>5846846
Applied mathematics is still mathematics.

>>5855323
>If your solution isn't simple you should find a better solution until you can't simplify it any further.

How do you measure the simplicity of a solution?

>>5846718
Who are you quoting?

>>5853690

That's weird, the DE class I took was also filled with engineers but they loved the class. We studied together for the final.


I'm a CS major, so not an engineer "defending his degree" or anything like that.

>>5856992
no, it's not.

especially not what they teach you in HS.

I was stoned off my ass the whole class, never did any homework, and still aced that class and the BC exam.

calculus is WAAAAAY more "hands on" than most mathematics.

if they taught algebra and geometry properly in school, that'd be about the only thing I'd say could be challenging about elementary mathematics

>>5838658
Corollary:
The simplest solutions are the hardest to find

>>5860731
What did you learn in your DE class?

>>5861100
Then why are they called "simple"?

>>5862937
why are they the 'hardest'?

>>5862941
Because of their resistance to change under force.

>>5838658
>that is what stupid people believe

>>5862937
Simple describing ease at which the equation can be done once found. Hardest describing the difficulty to find the equation that solves the problem.

>>5843212
Sure somebody is buttmad for being stupid.

>>5862937
They contain less fancy mathematical symbols.

>>5864844
Does that include numbers?

>>5866013
Only if you use a nonstandard font.

>>5843252
This guy has pretty much a premier attitude. Do what you want, do your best and if needed just grind.

>>5838658
OP's picture should be "first rule of high school maths" instead of "first rule of actual maths."

In real maths, if it seems easy and seems to just work, chances are you're doing it right. In high school maths they overcomplicate things and rely too heavily on a student's willingness to rote, it's an evil, evil thing.

http://www.maa.org/devlin/lockhartslament.pdf

>>5843185
gr8 b8 m8

>>5855569
>Why is the school system aimed at retards nowadays?
Because most educators assumption of students is that they're retarded memory retaining machines, especially true in non-tertiary education where the educators feel they're on top of a hierarchy with the students at the bottom. It doesn't help that everyone thinks Asians (actual Asians, ie born in Japan, China and Korea) are "smart," and then the west tries to emulate that "smartness" by following their system: which is essentially everything wrong with western education thrown into overdrive. Asians are smart though... when you only look at their academic performance.

You'll find that only some university professors do this, not all. Others pretty much state in the first lecture: I'm sorry, certain students might not do well, because I don't expect anything to be memorised, but understood. To which a million foreign students sweat, call the professor racist for not following their preferred system, and then curse the students (ethnicity agnostic, but generally westernised) who excel at understanding as opposed memorisation. I've been told my high marks are ill gotten, because I put so little effort into "studying" (ie cramming).

My point is, learning at university is fun if you're lucky. NOTHING like high school. You might even like university, come fourth year you might even wish for more.

>>5843801
>Undergrad megalomaniacal elitist dick waver detected.

>>5866801
This. My university has a significant minority as Chinese ( I would say 40% ) and they mostly just rote all their shit and prepare like they are brainwashing themselves for a standardized exam. Most only care about their grades too ( as opposed to also caring about getting something out of the class ).

>>5843185
>Gauss said that if Euler's Identity was not immediately apparent to a student upon being told it, that student would never be a first-class mathematician.
Pfft, maybe if Gauss was teaching mathematics. I had some Pakistani guy whose classes went like this:

>And zis is euler and zis is equivalent. Remember zis, zis is important. Yoo wont be engineer, if zis is not remembered
>>Yeah... but why does it work? How does it work?
>NO, zis is proof *proceeds to write a whole whiteboard of mathematics*
>>Okay, can you explain that?
*room goes silent, students look at me as if I asked for each of us to be tortured, Pakistani tutor looks at me like an idiot*
>>Uh... I might just go get a breath of fresh air
My point is, mathematics teachers are fucking retarded. There's a reason they're mathematics teachers and not accomplished scientists or engineers. To this day, I believe my first year engineering mathematics teacher didn't understand what he was teaching, he just expected us to memorise it and rote learn every example. Obviously it's impossible to really "get" what's going on.

>>5866756
What fonts are standard?

>>5866824

You cannot expect to learn mathematics just by going to lectures and listening to your teacher's explanations. Mathematics requires a lot of hard work from the student itself, that means that a lot of self study is necessary in order to understand what you're being told.

>>5866824
>To this day, I believe my first year engineering mathematics teacher didn't understand what he was teaching

He probably didn't want to waste his time with you. A mathematician has better things to do than explaining simple basics to anti-intellectual engineering freshmen who don't even care about the math but only entered university for the money.

>>5867888
Only Arial.

>be engineer
>tfw only know up to vector calc, PDE theory, linear algebra, numerical analysis, and some probability + statistics (all applied math)
>normal fags thing I'm good at math

top lel

>>5848969
Galois was. Imagine what he would have accomplished if he lived beyond 21. I guess we'll never know, so the dick measuring is purely speculative.

>>5848346
I really like this proof, although I don't know if you're actually asking for a proof haha.

http://www.math.uiuc.edu/~dan/ShortProofs/Zorn.pdf

>>5854940
Tedious, not hard. Try proving Urysohn's Lemma from scratch, or the Stone-Weierstrass theorem through case construction first, that's the last area that I really consider more tedious than intellectually challenging. Once you get beyond the undergraduate analysis/algebra/topology/number theory, and past the first graduate class or two in each of those topics, you start getting into the good stuff.

>>5838658
I disagree

>>5869206
Thank you.

>>5869204
>Galois was.
How do you know this?