Algebra Problem

[Narmer]

I'm studying this:link

We we're given this example in class: (12)(23) = (123)
: (123)(132) = I.

Anybody know how this works?

 

[us3rnotfound]

jeez

 

[AMCRambler]

That's algebra??? Zoinks! I'm lost. Abelian? Bijective? Surjective? Tell me this is a college level course. If this is high school math, then I stink.

 

[Leros]

Originally posted by: AMCRambler
That's algebra??? Zoinks! I'm lost. Abelian? Bijective? Surjective? Tell me this is a college level course. If this is high school math, then I stink.

Algebra can actually get quite complex, but this looks nothing like the algebra I've taken in K-12. The only college algebra course I've taken is linear algebra and I haven't seen this so far in the course (I'm taking it now).

 

[RaistlinZ]

Eek, good luck with that sh*t.

 

[AMCRambler]

Originally posted by: Leros

Originally posted by: AMCRambler
That's algebra??? Zoinks! I'm lost. Abelian? Bijective? Surjective? Tell me this is a college level course. If this is high school math, then I stink.

Algebra can actually get quite complex, but this looks nothing like the algebra I've taken in K-12. The only college algebra course I've taken is linear algebra and I haven't seen this so far in the course (I'm taking it now).

Ok, now I don't feel quite so much like a monkey trying to do someone else's math homework!

 

[Pugnax]

Hah, this isn't that tricky once you get the idea. It's just basic functional composition.
So if you look at wikipedia example:
f of g= you get:

num - from g - to f
----------------------
1 - 2 - 2 (The number 5 maps to 2 in g, and 2 in f maps to 2)
2 - 5 - 4
3 - 4 - 5 (etc.)
4 - 3 - 1
5 - 1 - 3 (the number 5 maps to 1 in g, and 1 in f maps to 3)
---------------------

As for your example...I'm not sure of the notation...but basically follow the same idea. You'll need to construct two matrices and compose them together.

So from wikipedia, to find f: (1 3)(4 5) = ? we'd do:
First one is (x) (transition 1->3, 3 -> 1)
1 2 3 4 5
3 2 1 4 5

next (y) (transition 4 ->5, 5 ->4)
1 2 3 4 5
1 2 3 5 4

---
f=x of y
1 2 3 4 5
3 2 1 5 4
-----------
Steps:
- x - y
1 - 1 - 3
2 - 2 - 2
3 - 3 - 1
4 - 5 - 5
5 - 4 - 4

I think that's right. Hope it helps..

 

[rocadelpunk]

Originally posted by: Narmer
I'm studying this:link

We we're given this example in class: (12)(23) = (123)
: (123)(132) = I.

Anybody know how this works?

ooh you might get to do caley graphs, those were fun. Yah, this is function composition.

lets say that (123) = f and (132) = g

so you want to basically permuate all the numbers, lets start with 1

so reading right to left (b/c function composition) we find 1 which is equivalent to saying what happens with f(g(1))...well g(1) goes to 3 (the 3 to the right of the 1) so now we have f(3) and that three goes to 1...so basically if you start with 1 you end with 1 and it can be written as (1)

Now the same thing happens with the rest...we covered 1, so lets go find 2.

f(g(2)) = f(1) = 2 ...so again 2 goes to 2...(2)

f(g(3)) = f(2) = 3 ...(3)

so you could write it as (123)(132) = (1)(2)(3) or as your professor put it.

hope that helps somewhat.

and for the first one...lets start at 2 to spice things up : P

so f = (12) g = (23)

f(g(2)) = f(3) which is nothing so that's why you just have your 2 going to 3

now f(g(3) = f(2) = 1 so 3 goes to 1 ...i.e. (231) which says 1 goes to 2, 2 goes to 3 and three goes to 1

just thought I'd show you that you can write the things in different ways and have it mean the same thing.

 

[Narmer]

Thanks guys, I was able to figure it out. I really appreciate your help. I wish there was a Help forum for stuff like this cause I don't want to clutter the OT page.

 

[michaels]

Hey I have a guy on my aim list that will solve any math problem you throw at him. I paid him 5 bucks a pop to do several things for me. If you want I will give you his screen name.

 

[Narmer]

Originally posted by: michaels
Hey I have a guy on my aim list that will solve any math problem you throw at him. I paid him 5 bucks a pop to do several things for me. If you want I will give you his screen name.

How do you pay him?

 

[WombRaider]

i bet it's an aim bot.

 

[michaels]

paypal, and no he isn't a bot, it's an Asian guy. He did a few complete sections for me last semester.

 

[Narmer]

Originally posted by: michaels
paypal, and no he isn't a bot, it's an Asian guy. He did a few complete sections for me last semester.

Thanks a lot. But I want to struggle through this. I enjoy the pain and headache.

 

[michaels]

well it was a last resort for me.

 

[jamesbond007]

I found this place a few years ago and have really enjoyed the help provided here.

http://www.physicsforums.com/

Enjoy!

 

[George P Burdell]

I had this stuff in a combinatorics course three years ago and now I can't remember anything Well maybe it's not such a bad thing.