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Off-Topic Discussion => General Discussion => Topic started by: adwight on April 29, 2004, 09:24:14 pm

Title: Mathematical Induction, For God's Sake Help!
Post by: adwight on April 29, 2004, 09:24:14 pm
Well, in my Precalculus class we just got to the most confusing math concept I've ever seen, Mathematical Induction.  It involes series, and proving those series are true for all real positive integers.  Does anyone have notes or could walk me through on how to do this?  Its so bleeping confusing I have no idea where to begin.
Title: Mathematical Induction, For God's Sake Help!
Post by: Goober5000 on April 29, 2004, 09:28:31 pm
Induction is fun, but presented in the wrong way it can be confusing.  Try starting here:
http://en.wikipedia.org/wiki/Mathematical_induction
Title: Mathematical Induction, For God's Sake Help!
Post by: adwight on April 29, 2004, 09:33:40 pm
That helped a little but I still don't get the part past
"This is that statement for n = m + 1. Note that it has not been proved as true: we made the assumption that P( m ) is true, and from that assumption we derived P( m + 1 ). Symbolically, we have shown that:"

They don't look equal to me, unless im totally stupid.  Also, how can you think this stuff is fun?
Title: Mathematical Induction, For God's Sake Help!
Post by: phreak on April 29, 2004, 09:34:00 pm
isn't it a bit early to be starting math induction in precalculus?
Title: Mathematical Induction, For God's Sake Help!
Post by: Goober5000 on April 29, 2004, 09:40:21 pm
I would think so.  And it's only fun when you understand it. :p

Say you have two statements:
(a) X is true
(b) Y is true when X is true
You have no way of proving that Y is true directly, but if you can prove both (a) and (b), then "by induction" Y must also be true.

Now substitue X + 1 for Y in the above argument:
(a) X is true
(b) X + 1 is true when X is true
Since you can always count one number higher, you prove X is true for all counting numbers.
Title: Mathematical Induction, For God's Sake Help!
Post by: adwight on April 29, 2004, 09:50:12 pm
Well this is "Honors Precalculus".(AP Calc next year, yuck).  I think I sort of understand it, but if someone could take me step by step, over a messenger service or something, it would be quite helpful.
Title: Mathematical Induction, For God's Sake Help!
Post by: Goober5000 on April 29, 2004, 09:54:11 pm
ICQ.  Number in profile.
Title: Mathematical Induction, For God's Sake Help!
Post by: Stealth on April 29, 2004, 09:55:51 pm
goober's a good man *thumbs up*
Title: Mathematical Induction, For God's Sake Help!
Post by: adwight on April 29, 2004, 09:56:17 pm
Sorry man, I don't have ICQ.  I have MSN and Aim.

MSN is [email protected]
AIM is tsthor07
Title: Mathematical Induction, For God's Sake Help!
Post by: Goober5000 on April 29, 2004, 09:57:49 pm
And you don't seem to be on. ;)
Title: Mathematical Induction, For God's Sake Help!
Post by: adwight on April 29, 2004, 10:01:04 pm
Well I'm on my AIM now.  I've been on MSN for quite a while.
I'm stupid, its TSThor7 my bad.
Title: Mathematical Induction, For God's Sake Help!
Post by: mikhael on April 29, 2004, 10:43:56 pm
*heh* Induction is fun--when you're dealing with it in Calculus.

It stops being fun when you start using it in set theory and counting and all those other discrete maths topics.

Where's a vomit smiley when you need one?
Title: Mathematical Induction, For God's Sake Help!
Post by: phreak on April 29, 2004, 10:45:50 pm
i'm taking discrete math in the fall, my linear algebra prof said were going to do a lot of induction.

theres a few vomit smilies here
http://www.mysmilies.com/?cat=obscene&page=1
Title: Mathematical Induction, For God's Sake Help!
Post by: adwight on April 29, 2004, 11:01:51 pm
Goober is a stud, he just spent the last hour helping me understand how to do it, and I actually know how.  Thank you so much Goober.
Title: Mathematical Induction, For God's Sake Help!
Post by: Goober5000 on April 29, 2004, 11:05:09 pm
You're welcome. :)
Title: Mathematical Induction, For God's Sake Help!
Post by: mikhael on April 29, 2004, 11:14:14 pm
Quote
Originally posted by PhReAk
i'm taking discrete math in the fall, my linear algebra prof said were going to do a lot of induction.


You poor, poor bastard. I've got an A so far, but I'll be honest: I make it up as I go along and the teacher just slaps an A on it.
Title: Mathematical Induction, For God's Sake Help!
Post by: phreak on April 30, 2004, 12:08:58 am
luckily for me my Discrete Math prof speaks english as opposed to something else.  My data structures prof wasn't a native speaker and when you get into technical subjects it can be difficult to convey ideas

Quote

You know sorting? no?  Well all you do is put all the skilled laborers over here and all the unskilled laborers over there
Title: Mathematical Induction, For God's Sake Help!
Post by: Setekh on April 30, 2004, 01:57:16 am
Ah, I'm too late! And induction is actually something I'm good at. Mega props to you, Goober, for stepping in there. :nod::yes:
Title: Mathematical Induction, For God's Sake Help!
Post by: Goober5000 on April 30, 2004, 02:30:17 am
Thanks. :) I'd have contacted you about your math assignment except I was asleep at the time. ;)
Title: Mathematical Induction, For God's Sake Help!
Post by: kode on April 30, 2004, 05:53:57 am
I did some induction in two of my previous math courses. proving the fibonacci numbers and other simple stuff. my fav part was when the professor proved that there are as many even natural numbers as there are natural numbers...
Title: Mathematical Induction, For God's Sake Help!
Post by: DragonClaw on April 30, 2004, 06:31:55 am
Heh. We already learned induction in my Algebra II class.
Title: Mathematical Induction, For God's Sake Help!
Post by: adwight on April 30, 2004, 03:57:34 pm
Thanks to u Goober, I got a 10/10 on my assignment.  Thanks bro.
Title: Mathematical Induction, For God's Sake Help!
Post by: Goober5000 on April 30, 2004, 04:13:27 pm
Cool. :yes: You're welcome. :)
Title: Mathematical Induction, For God's Sake Help!
Post by: Col. Fishguts on April 30, 2004, 04:45:12 pm
Quote
Originally posted by PhReAk
i'm taking discrete math in the fall, my linear algebra prof said were going to do a lot of induction.

theres a few vomit smilies here
http://www.mysmilies.com/?cat=obscene&page=1


YUCK ...been there, done that.....and hated it passionately

"How many ways are there to [insert stupid expression including stuff like arranging/coloring/partitioning/counting] ?"

And group theory is pretty abstract, but not as boring as the counting problems.

Anyway...good luck.
Title: Mathematical Induction, For God's Sake Help!
Post by: kode on April 30, 2004, 04:59:37 pm
me, I must say that I like discrete maths more than any other branch of math I've had the joy to encounter so far. at least you don't have to integrate and stuff all the time.
Title: Mathematical Induction, For God's Sake Help!
Post by: adwight on April 30, 2004, 10:13:53 pm
I get the feeling that I've only begun to get my feet wet with this math stuff.
Title: Mathematical Induction, For God's Sake Help!
Post by: mikhael on April 30, 2004, 10:28:56 pm
Well, considering the work of Godel, pretty much no matter where you look in math, you'll only be "getting your feet wet". ;)

Math is beautiful and perfect and completely impossible to know completely. ;)
Title: Mathematical Induction, For God's Sake Help!
Post by: Langy on April 30, 2004, 11:24:58 pm
Quote
at least you don't have to integrate and stuff all the time.


Bah. Integration=fun. Not all that difficult, either, when you know the formulas.
Title: Mathematical Induction, For God's Sake Help!
Post by: Kazan on April 30, 2004, 11:46:26 pm
integration is easy when you're not integrating Sin^3(x)*Cos^7(x) - or some fractional ****
Title: Mathematical Induction, For God's Sake Help!
Post by: kode on May 01, 2004, 04:37:44 am
Quote
Originally posted by Kazan
integration is easy when you're not integrating Sin^3(x)*Cos^7(x) - or some fractional ****


which was practically all we did under the analysis course.
Title: Mathematical Induction, For God's Sake Help!
Post by: mikhael on May 01, 2004, 08:42:06 am
Integration is pretty easy as long as you A) remember the chain rule and B) remember how to derive the trigonmetric integrals. :D