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Author Topic: There's gotta be some math whizzes in here.  (Read 7953 times)

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sparky5856

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There's gotta be some math whizzes in here.
« on: October 01, 2012, 03:53:06 pm »
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I guess we can use this thread to talk about anything math-related, cause math is fun amirite?

But while I do think math is fun, I'm stuck on a concept involving strong mathematical induction. Specifically, I'm trying to prove inequalities such as 2n + 1 ≤ 2n. Anyone know how to approach this? I know the base case (for n = 3), it's the induction step that I'm stuck on.
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DStu

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Re: There's gotta be some math whizzes in here.
« Reply #1 on: October 01, 2012, 04:00:28 pm »
+1
So let n be true blabla

n+1:
2(n+1)+1
=(2n+1)+2
\leq 2^n+2  by induction
= 2^{n+1}(1/2+2^{-n})

1/2+2^{-n}\leq 1 for n\geq 1
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Cuzz

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Re: There's gotta be some math whizzes in here.
« Reply #2 on: October 01, 2012, 08:39:30 pm »
+2
sparky, are you trying to get us to do your homework?  ;D
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sparky5856

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Re: There's gotta be some math whizzes in here.
« Reply #3 on: October 01, 2012, 09:21:32 pm »
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...maybe <.< I know I know, I should be finding the scum. That's much more fun.

Hey, there's gotta be some gateway thread into the fun world of maths.
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ehunt

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Re: There's gotta be some math whizzes in here.
« Reply #4 on: October 02, 2012, 12:47:22 am »
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I suggest math.stackexchange.com for this.
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ehunt

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Re: There's gotta be some math whizzes in here.
« Reply #5 on: October 02, 2012, 12:48:35 am »
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(clarification I don't mind it on f.ds either, just  saying that other site is really good.)
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Cuzz

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Re: There's gotta be some math whizzes in here.
« Reply #6 on: October 02, 2012, 07:35:19 pm »
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So what other math people do we have around here? I'm in grad school at the moment, working in complex dynamics (hence the avatar).
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cayvie

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Re: There's gotta be some math whizzes in here.
« Reply #7 on: October 02, 2012, 07:38:33 pm »
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Quote from: Cuzz on October 02, 2012, 07:35:19 pm
So what other math people do we have around here? I'm in grad school at the moment, working in complex dynamics (hence the avatar).

maaaaan i took fractals & dynamic systems in high school; that class was awesome.
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Captain_Frisk

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Re: There's gotta be some math whizzes in here.
« Reply #8 on: October 02, 2012, 07:45:48 pm »
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Bs ee here, so I took my fair share of math.
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shraeye

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Re: There's gotta be some math whizzes in here.
« Reply #9 on: October 02, 2012, 10:53:45 pm »
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I'm grad school math as well.  Currently studying Pfister forms in characteristic 2.
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Axxle

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Re: There's gotta be some math whizzes in here.
« Reply #10 on: October 02, 2012, 10:54:39 pm »
+3
Give a man a math and he'll pass his homework.

Teach a man to math and he'll pass his exams.
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ConMan

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Re: There's gotta be some math whizzes in here.
« Reply #11 on: October 03, 2012, 12:34:32 am »
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Maths/stats background here. And I do so love playing around with mathematical oddities.
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sparky5856

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Re: There's gotta be some math whizzes in here.
« Reply #12 on: October 03, 2012, 12:45:50 am »
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If anyone is interested in quirky mathematical tidbits I recommend checking out Numberphile on Youtube. I was considering submitting a yahtzee video for them; I COULD attempt a yahtzee with 5 thirty-sided dice, but that would take way too long. >_<

My background is computer science btw. The "homework", I'll call it, was for a course concerning the mathematical foundations of computer science. Deep stuff.
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Axxle

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Re: There's gotta be some math whizzes in here.
« Reply #13 on: October 03, 2012, 01:51:18 am »
+1
Quote from: sparky5856 on October 03, 2012, 12:45:50 am
If anyone is interested in quirky mathematical tidbits I recommend checking out Numberphile on Youtube. I was considering submitting a yahtzee video for them; I COULD attempt a yahtzee with 5 thirty-sided dice, but that would take way too long. >_<

My background is computer science btw. The "homework", I'll call it, was for a course concerning the mathematical foundations of computer science. Deep stuff.
Also: Vihart!
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SirPeebles

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Re: There's gotta be some math whizzes in here.
« Reply #14 on: October 03, 2012, 06:23:32 pm »
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I'm currently doing a postdoc in math.  I study homological algebra, rings, and category theory.
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Captain_Frisk

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Re: There's gotta be some math whizzes in here.
« Reply #15 on: October 03, 2012, 06:38:46 pm »
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Cuzz

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Re: There's gotta be some math whizzes in here.
« Reply #16 on: October 03, 2012, 10:49:55 pm »
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Quote from: Captain_Frisk on October 03, 2012, 06:38:46 pm
Quote from: Axxle on October 03, 2012, 01:51:18 am
Also: Vihart!

Sigh....

Yeah, something about her just kinda bugs me. But if it gets people more interested in math then I can't really complain.
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Cuzz

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Re: There's gotta be some math whizzes in here.
« Reply #17 on: October 03, 2012, 10:50:59 pm »
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Quote from: cayvie on October 02, 2012, 07:38:33 pm
Quote from: Cuzz on October 02, 2012, 07:35:19 pm
So what other math people do we have around here? I'm in grad school at the moment, working in complex dynamics (hence the avatar).

maaaaan i took fractals & dynamic systems in high school; that class was awesome.

Your high school sounds awesome.
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Captain_Frisk

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Re: There's gotta be some math whizzes in here.
« Reply #18 on: October 03, 2012, 11:14:41 pm »
+2
Quote from: Cuzz on October 03, 2012, 10:49:55 pm
Quote from: Captain_Frisk on October 03, 2012, 06:38:46 pm
Quote from: Axxle on October 03, 2012, 01:51:18 am
Also: Vihart!

Sigh....

Yeah, something about her just kinda bugs me. But if it gets people more interested in math then I can't really complain.

That was a dreamy sigh.  Girls talking about math.....
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Eevee

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Re: There's gotta be some math whizzes in here.
« Reply #19 on: October 03, 2012, 11:18:30 pm »
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Quote from: Captain_Frisk on October 03, 2012, 06:38:46 pm
Quote from: Axxle on October 03, 2012, 01:51:18 am
Also: Vihart!

Sigh....
Uuh uuh, I know this one! I just (literally 5 minutes ago) saw my first Vihart-video (http://www.youtube.com/watch?v=DK5Z709J2eo&feature=share, my cousin linked it on facebook). Pretty awesome!
« Last Edit: October 03, 2012, 11:54:58 pm by Eevee »
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ehunt

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Re: There's gotta be some math whizzes in here.
« Reply #20 on: October 04, 2012, 12:05:31 am »
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Quote from: Cuzz on October 02, 2012, 07:35:19 pm
So what other math people do we have around here? I'm in grad school at the moment, working in complex dynamics (hence the avatar).

number theory grad student
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cayvie

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Re: There's gotta be some math whizzes in here.
« Reply #21 on: October 04, 2012, 01:13:05 am »
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Quote from: Cuzz on October 03, 2012, 10:50:59 pm
Quote from: cayvie on October 02, 2012, 07:38:33 pm
Quote from: Cuzz on October 02, 2012, 07:35:19 pm
So what other math people do we have around here? I'm in grad school at the moment, working in complex dynamics (hence the avatar).

maaaaan i took fractals & dynamic systems in high school; that class was awesome.

Your high school sounds awesome.

NCSSM

it was
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qmech

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Re: There's gotta be some math whizzes in here.
« Reply #22 on: October 04, 2012, 04:22:29 am »
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This is late, and DStu already covered the mechanics, but here's how to think of mathematical induction: it's a magic tool that lets you assume you can solve all smaller instances of problems ("by induction" being the magic words).  So I'd write 2n = 2.2n-1 >= 2(2(n-1)+1) = 4n-2 >= 2n+1 (for n >= 4).  I find the switch in perspective to focus on the case you're trying to prove, rather than the one you already know, helpful (it feels more stable to be "pulling up" to a goal rather than "pushing out" from a start point).
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Ozle

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Re: There's gotta be some math whizzes in here.
« Reply #23 on: October 04, 2012, 06:04:55 am »
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Is the answer 6?
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Cuzz

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Re: There's gotta be some math whizzes in here.
« Reply #24 on: October 04, 2012, 07:22:43 am »
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Quote from: Ozle on October 04, 2012, 06:04:55 am
Is the answer 6?

You clearly forgot to carry the e.
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