Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Topic: What difficulties encountered by beginners in abstract algebra?
Replies: 17   Last Post: Jan 20, 2013 6:16 AM

 Messages: [ Previous | Next ]
 Ken.Pledger@vuw.ac.nz Posts: 1,412 Registered: 12/3/04
Re: What difficulties encountered by beginners in abstract algebra?
Posted: Jan 9, 2013 2:35 PM

In article <kckcnc\$vh2\$2@dont-email.me>,

> ....
> The big speed bump for me is thinking about composition of permutations. The
> notation seems to get me wrapped around the axle.

Here's a way to explain that. Write a little 1 as superscript just
before the first cycle. (I use Cauchy's original left-to-right cycle
notation.) Then ask "What does that cycle do to 1?" If it maps 1 to 6,
say, then write a little superscipt 6 between the first and second
cycles; and ask "What does the next cycle do to 6?" Keep going until
you end up with 4, say; then begin writing the answer as (1 4 .

Now rub out all the old superscripts and start again with a little 4
at the beginning, etc. Students seem to get the idea very quickly this
way.

Ken Pledger.