Print

Please login or register.
1 Hour 1 Day 1 Week 1 Month Forever
Login with username, password and session length

[sparky5856]

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.

[DStu]

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

[Cuzz]

sparky, are you trying to get us to do your homework? 

[sparky5856]

...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.

[ehunt]

I suggest math.stackexchange.com for this.

[ehunt]

(clarification I don't mind it on f.ds either, just  saying that other site is really good.)

[Cuzz]

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).

[cayvie]

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.

[Captain_Frisk]

Bs ee here, so I took my fair share of math.

[shraeye]

I'm grad school math as well.  Currently studying Pfister forms in characteristic 2.

[Axxle]

Give a man a math and he'll pass his homework.

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

[ConMan]

Maths/stats background here. And I do so love playing around with mathematical oddities.

[sparky5856]

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.

[Axxle]

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!

[SirPeebles]

I'm currently doing a postdoc in math.  I study homological algebra, rings, and category theory.

[Captain_Frisk]

Also: Vihart!

Sigh....

[Cuzz]

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.

[Cuzz]

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.

[Captain_Frisk]

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.....

[Eevee]

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!

[ehunt]

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

[cayvie]

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

[qmech]

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 = 2.2^n-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).

[Ozle]

Is the answer 6?

[Cuzz]

Is the answer 6?

You clearly forgot to carry the e.

[Ozle]

Is the answer 6?

You clearly forgot to carry the e.

7 then?

[Toolshed113]

It's amazing how quickly your math skills deteriorate once you leave the scholastic world. I was a lowly computer engineering major in undergrad, but I still had to take a decent amount of math. Now that I actually have a software engineering job I can't remember the last time I used ANY of the higher level math I had to take (calc 2+, diff eq, that stuff). It's very sad considering I graduated 2 years ago.

[Tables]

Maths Undergrad here, in my final year gunning only for a lowly 2:1. But apparently that still makes me better at maths than most people .