In article <firstname.lastname@example.org>, email@example.com (Michael Stemper) wrote:
> .... > 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.