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/sci/ - Science & Math

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4370512 No.4370512 [Reply] [Original]

>Starting engineering degree this year
>At a fairly prestigious university, one of the best in the country, at the very least in the top three.
>My math isn't up to par, so I take a short math bridging course to kick it up to speed
>Haven't done math in over a year, and we're doing implicit differentiation and stuff
>It's tough, but I'm getting by
>Suddenly inductions
>Have no fucking idea what the tutor is saying during the seminar
>Call him over after he's done, explain that I don't really understand the concepts he explained
>He starts explaining it to me, but very poorly, just doing questions and reading out what he's writing, albeit doing it all step by step so its easier to understand
>Tell him that I don't understand how it's all being done, and if he could explain it in more detail
>He looks up for 4 seconds, and sighs a breath of 'how do you not understand this?'

I'm in your fucking class because I'm shit at math, you fucking asshole. Not everyone spent their degree being a useless shit and now has to resort to being a math tutor for the learning department to earn a buck. Fuck you.

Useless teachers/tutors general

>> No.4370520

inductions?

wtf is this shit.

>> No.4370523

>>4370520
It's just a way to prove certain propositions.

>> No.4370527

>>4370523
yah I wouldnt be fucking worrying about that shit as an engineer

fucking LOL

>> No.4370524

people still rely on Ta's and profs for help? I never ask them for help because I know they don't give a fuck. I'd rather ask a friend or try to learn off the internet.

>> No.4370530

>>4370524
yah it's pretty true.

TA's and profs are for the most part, fucking useless.

some of the shit they teach isn't even what they're interested in and just kind of read from the textbook.

>> No.4370531

>>4370527
I've been told by fourth year students that it's pretty vital for a lot of the math classes in my degree, particularly in first year.

>> No.4370535

>>4370520
http://en.wikipedia.org/wiki/Mathematical_induction

>> No.4370534

>>4370531
what the fuck. youre engineering correct?

no fucking idea what theyre talking about

>> No.4370538

>>4370534
Yeah, chemical.

>> No.4370542

>>4370524
>>4370530
this. i had some good professors that understood the course is an introductory course and they actually took the time to explain shit in detail.

then there are assholes that think introductory course means cram as much shit into the students as fast as possible and only derive equations during class time. i have considered grad school, but knowing that if i went for a doctorate and had to work with one of these assholes, i'd rather stick to just a masters and call it quits.

>> No.4370548

>>4370538
then why the fuck are you taking a proofs class?

i'm in my second semester of junior year working towards my mechanical engineering degree and proofs have never come in handy yet.

>> No.4370549

you're at university of illinois, aren't you?

>> No.4370550

lol. As an engineer you really don't need to do any kind of proofs.
That being said, induction is not a really hard concept.

>> No.4370554

why do engineers need to know induction?

also it isn't an especially easy concept to understand without good examples, op.

>> No.4370560
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4370560

>Engineers
>Requiring any form of logical reasoning

>> No.4370562

>>4370554
they don't, op must have got trolled.

i'm curious if he put off calc to take the bullshit proofs class, too. if he did then he went full retard, because the calculus is directly and indirectly a prerequisite for nearly every engineering class, so now he's going to be behind.

>> No.4370566
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4370566

>>4370560
>proofs
>not biology tier

>> No.4370569

>2012
>Not understanding inductions

It's a fucking cake breeze. No wonder your tutor was frustrated.

>> No.4370576

>Not everyone spent their degree being a useless shit and now has to resort to being a math tutor for the learning department to earn a buck.

Maybe you should major in art instead.

>> No.4370577

You prove the condition is true for the case n=1.

Assume it's true for n=k.

Prove it's true for n=k+1, given your assumption that it is true for n=k.

Now, set k=1. We know it's true for this, then given you've proven it's true for k+1, given that it's true for k, it's also true for n=2.

Now, set k=2. We know it's true for this, then given you've proven it's true for k+1, given that it's true for k, it's also true for n=3

...

>> No.4370585

Now, we HAVE NOT actually shown that it works for every n, we are just saying that when it DOES work for n, that will make it also work at n+1, then we will have a proof.

So, we have 2 separate things.

1. We KNOW it works at 1. 1 = 1(1+1)/2.
2. We WANT it to work at n: 1 + 2 + ... + n = n(n+1)/2

So, now let's show that IF IT DOES work at n, it will ALSO work at n+1.

How do we do this? That will depend on the actual problem and the method can change, but in this case it goes like this:

At n, we have 1 + 2 + ... + n = n(n+1)2
At n+1, we have 1 + 2 + ... + n + (n+1) = (n+1)((n+1)+1)/2

Now, looking at the bottom equation, every term on the LEFT side except (n+1) is the LEFT side of the top equation, so we can substitute the RIGHT side of the top equation in to the bottom equations:

n(n+1)/2 + (n+1) = (n+1)(n+2)/2

If this equation is true, then we have shown that IF

1 + 2 + ... + n = n(n+1)/2 THEN

1 + 2 + ... + n + (n+1) = (n+1)((n+1)+1)/2.

Well, we know that it works at n = 1, so it must work at 1+1 = 2. Then it must work at 2+1 = 3, etc. It works for all numbers.

>> No.4370584
File: 27 KB, 500x574, 1289015171771.jpg [View same] [iqdb] [saucenao] [google]
4370584

>>4370566

>biology scum
>not still superior to engineers

>> No.4370581

Okay OP, here's how induction works.

Let's say you have some property, and you're trying to see if the property is true or not.

For example, consider this property:

if you add up all of the numbers from 1 to n, the result will be equal to (n(n+1))/2.

Now, is this true or not?

To use induction, you see if it works for a base case (n=1).

Add up all the numbers from 1 to 1: it's just 1.

Try plugging 1 in to that other expression:

1(1+1)/2 = 1. Hey, it works.

Now, let's say it DOES work for some n. We don't know if it does or not, but what we're going to do is show that IF it happens to work at n, then it WILL work at n+1.

Now, let's say we were able to show this. What does that mean? Well, if n=1, then we KNOW that it works at 1+1, which is 2. Well hey, since it works at 2, we KNOW it has to work at 2+1 = 3. From this, you can see it will work at every number above 1.

>> No.4370589

>>4370585

>It works for all numbers.

No.

>> No.4370590

>>4370562
>proofs class
Im allways baffled by the fact, that there are special proofs classes. If you do math/physics/perhaps cs, don't you just do proofs in your regular math classes? Why is there a need for a proofs class?

>> No.4370597

>>4370548
I'm not taking a proofs class. It's just a bridging class over the course of 2 weeks which covers a lot of different topics. Tomorrow we're doing polynomials and rational functions, which will be much easier. I think it's just there to get you into the 'math mind' after break, and to help with people like me who are exceptionally bad at it.

>>4370549
Not in the US.

>> No.4370598

>>4370589

replace all cases of "number" with natural number, I wasn't trying to give a formal proof.

>> No.4370601

>>4370598

Yeah, but we don't want to give OP the wrong idea. Not just trying to be a dick.

>> No.4370603

>>4370601

Saying "No." is just being a dick. You should have explained that it only works from your base case up or something.

>> No.4370608

>>4370585
Wow, this actually helped a lot. Thanks bro.

>> No.4370613

>>4370608

There's another property you can practice with:

<div class="math">1^3 + 2^3 + ... + n^3 = (1 + 2 + ... + n)^2</div>

It makes use of the one I showed.

>> No.4370617

>>4370608

I know what it's like, I was actually taught induction in 3 different classes and while I could do it, I didn't understand why until the 3rd time.

>> No.4370618

Op is a butthurt pleb with an IQ below 100
>taking maths when you don't understand shit

>> No.4370620

>>4370618
I know I'm not that bright, but I have dedication, and that's all you really need to get a degree nowadays.

>> No.4370625

>>4370620
Everybody gets a medal.

>> No.4370626

>>4370620
around here they teach inductions when you are 13.
It's either burger flipping for you or a woman's studies/english degree

>> No.4370633

>>4370626
I was studying chemistry last year, and I achieved HD average. I don't think I'm a moron, but seriously you sound like a pretentious asshole.

>> No.4370634

>>4370633

>but seriously you sound like a pretentious asshole.

Welcome to /sci/.

>> No.4370639

>>4370590 Why is there a need for a proofs class?

Because not everyone has an inferiority complex and feels the need to prove something to show they're a man. It lets these people stay away and stop annoying normal people with their incessant bullshit.

>> No.4370640

>>4370626
>inductions at 13
>13

LMAO where do you live? America?

>> No.4370641

>>4370633
>I achieved HD average

God my sides

>> No.4370651

>>4370641
not OP, but whats funny about that?

>> No.4370662

>>4370590
You need some kind of logical foundation to make sure you prove things correctly, a class where you learn things like induction and proof by contradiction. It's usually combined with some other types of discrete math. My class did some basic combinatorics, number theory, and set theory along with the logic stuff. For an engineer there is basically no need to know any of this stuff. Induction, however, is a very intuitively clear concept.

>> No.4370667

>>4370639
Yeah who needs mathematical rigour, what has it ever done for us?!?

>> No.4370687

University of Sydney amirite?

>> No.4370692

>>4370687
Nice. What gave it away?

>> No.4370695
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4370695

>mfw I'm a practicing chemical engineer for years and the only maths I do is on some excel spreadsheets and everyone treats me like I'm some mathematical genius

>> No.4370697

>>4370692

I'm in the maths ext1 bridging course too, so the whole "implicit > induction" thing.

Also engineering

>> No.4370698

>>4370697
You done question 4 on the worksheet?

>> No.4370700

>>4370698

Only part i)

>> No.4370711

>>4370700
Heh, same here.

>> No.4370714

>>4370711

I'm also doing ChemE, who's your tutor?

>> No.4370715

>>4370714
Do you do mornings or evenings?

>> No.4370717

ITT: Two brofags meet and realize they go to the same school.

They become best friends and have gay buttsecks.

>> No.4370718

>>4370715

Mornings

>> No.4370720

>>4370717

They also are doing the same engineering, a match made in buttsex

>> No.4370723
File: 13 KB, 203x152, _40127544_students_203152.gif [View same] [iqdb] [saucenao] [google]
4370723

>>4370718
Neil

>> No.4370729

>>4370723
Also if you're in my class I bet you're either the guy with the curly shaggy hair or the bigger guy who sits opposite him.

>> No.4370733

>>4370729

Not in your class unfortunately.

>> No.4370736

>>4370733
Oh well. Could have been a beautiful love story.

>> No.4370738

>>4370729

Heres a clue, I'm asian

>> No.4370740

>>4370738
Wait, so are you in my class or not?

>> No.4370742

>>4370740

Nah, I'm not

>> No.4370747

>>4370742
Might see you in our classes then.

Also post your answers to the homework. DW about Q4 though, don't give a shit if I'm wrong with that one.

>> No.4370748

>Working on my PhD in math at my state school (whatevs)
>in my spare time I tutor remedial math to help those less gifted than myself (and the freshman girls are bangin')
>the subject we are going over is basic differentials
>finish the seminar and the kids break off into groups to work on some basic examples
>everyone seems to be getting it but one socially awkward kid is sitting in the corner, not in a group
>I see that he is really struggling so I go over to help him out
>"Hey!" I say. "Need some help?"
>"I-I-I d-d-don't understand the err... duction... you making..."
>The kid stares blankly at his feet
>"Well, here," I say, "Let's work an example together"
>several examples later the kid is clearly frustrated and still not getting it
>"Maybe you should try working these examples out with some classmates, I'm sure there are some that have the same issues as you," I suggest.
>His face gets flush red and the corner of his mouth opens, his eyes still fixed on the floor between his shoes
>"f-f-fcking... t-top engineering school.... sshole n-n-no good t-tutor"
>the kid storms out of the room
>Oh well, time to help the Pi Phi sluts

>> No.4370753

>>4370747
Actually don't worry about it, the questions were really easy and I doubt I'm wrong.

>> No.4370760

>>4370512
>Starting engineering degree this year

Stopped reading.
<------/cm/

>> No.4370761

>>4370753

No problem bro, really didn't want to type it all up anyway.

>> No.4370765

>>4370761
Actually, what did you get for 3. b)? Did you get some whacked long as shit answer?

>> No.4370772

>>4370753

yep, I got a long answer, look at q.3's answer on pg 89, got that, had to take a glance at it to do it right.

>> No.4370777

>>4370772
Cheers bro. I'll see you around.

>> No.4370778

>>4370748
That is such an unfair caricature of your student. First you tell us that he's socially inept, and then that he can't understand such basic stuff as induction? Come on, no one can't be that stupid. Next you'll accuse him of starting a thread in some board whining about how much his life sucks and that the world doesn't revolve around his low intellect. Not cool man, that's really dishonest and unfair for your student, he can't be such a fucking loser.

>> No.4370780

>>4370585
If I remember correctly the methodology for induction is as follows:
take sum of 1 to n = (n(n+1))/2 as example
(sum of 1 to n is also called "n!")
1) prove for n= 1 as shown in that post
2) now write down what it would look like when n = a number k, and write that you assume it's true
in your case 1 + 2 + ... + k = (k(k+1)))/2
3) write again the expression but n = k+1
1+ 2 + ... + k + (k+1) = ((k+1)(k+2))/2
4) substitute k! on left hand side of 3) by right hand side of 2), since we know theyre equal
5) (k(k+1)))/2 + (k+1) = ((k+1)(k+2))/2. work out until both sides are the same thing, proving theyre equal
6) now you have to write some bullshit sentence down like "by the powers invested in me by math, I hereby declare this statement proven by induction. status: Proofasaurus Rex

They might also ask you the problem in a word problem format, like prove that bla is divisible by nine, then you have to set the right hand side for yourself.

>> No.4370784

>>4370777

Laters, good luck for engo

>> No.4370785

>>4370778
>Next you'll accuse him of starting a thread in some board whining about how much his life sucks and that the world doesn't revolve around his low intellect.

Whoa, whoa, slow down bro. I said he was a socially inept retard, but I'd never go that far.

>> No.4370791
File: 96 KB, 443x412, internet tough guy.jpg [View same] [iqdb] [saucenao] [google]
4370791

>>4370778
You sure told him.

>> No.4370828

This just in: engineers need induction more than real mathematicians because engineering relys on numerical approximations, which for the most part can only be verified using induction and which screw up with a degree of oddness comparable to their usefulness.

Have fun drawing pictures for the rest of your life OP.

True story: Physics major here (like an engineer only smart) see induction for the first time this year. It's literally plugging your equation back into itself. I can't believe people actually have difficulty with this.

Anyways, enjoy paying for a good education you're obviously too stupid to take advantage of, I'm going to go back to studying for the hard versions of your classes.

>> No.4370838

My calculus tutor is Chinese and noone understands what the fuck he's saying, all you can make out is "cosane", "sane" and "dorta", so if you're having problems just go on Khan Academy, that's what I do.

>> No.4370845

>>4370828
> which for the most part can only be verified using induction
Heh. Engineers verifying stuff...