I've found Sage a great complement to my abstract algebra course.
Based on last fall's course (2008) I created a primer of Sage commands
useful for learning group theory.

http://abstract.ups.edu/sage-aata.html

I'll likely update it after this fall's course ends and then expand it
this spring when I teach rings, fields, etc.  I'll greatly expand my
use of Sage in my linear algebra course which I will teach again this
spring after a bit of a break.  I've also found Sage's 3D plots
extremely useful for teaching multivariate calculus.

One important feature to realize about Sage is that it can often
represent mathematical objects exactly.  For example, the null space
(kernel) of a matrix is a *vector space*, not just a pile of basis
vectors.  Then you can do many of the things you might do with a
vector space, like asking for its dimension, or intersecting it with
another vector space.  I find this a valuable feature when using Sage
with students.

Rob
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