Making Algebra Less "Abstract"

[bretbenesh]

I am teaching abstract algebra next semester, and I have decided to focus on 9 10 finite groups at the beginning of the semester. These groups are:

1. Cyclic group of order 3
   
2. Cyclic group of order 6
   
3. Cyclic group of order 7
   
4. Dihedral group of order 6
   
5. Dihedral group of order 8
   
6. Symmetric group of order 6
   
7. Symmetric group of order 24
   
8. Alternating

Comments

[anonymous]

I'd add in Z_2 x Z_2 so students don't think that all abelian groups are cyclic. Plus the automorphisms of this group are isomorphic to S_3 (a nice exercise for a good student).

--Jill D.

[bretbenesh]

Jill,

This is a fantastic idea---I am sorry I missed it in my planning. I will give them something akin to two coins for the physical model.

I appreciate the help!
Bret