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Re: What difficulties encountered by beginners in abstract algebra?
Posted:
Jan 9, 2013 2:35 PM
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In article <kckcnc$vh2$2@dont-email.me>,
mstemper@walkabout.empros.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.
Ken Pledger.
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